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Worksheet
A chapter that explores sequences where each term after the first is obtained by adding a constant difference, focusing on their properties, nth term, and sum formulas.
Arithmetic Progressions - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Arithmetic Progressions from Mathematics for Class X (Mathematics).
Questions
Define Arithmetic Progression (AP) and explain its significance with a real-life example.
Think about situations where a fixed amount is added or subtracted regularly.
Find the 10th term of the AP: 3, 7, 11, 15, ...
Use the formula for the nth term of an AP: a_n = a + (n-1)d.
How many terms of the AP: 9, 17, 25, ... must be taken to give a sum of 636?
Use the sum formula for AP and solve the resulting quadratic equation.
The first term of an AP is 5, the last term is 45, and the sum is 400. Find the number of terms and the common difference.
First find the number of terms using the sum formula, then find the common difference using the nth term formula.
Find the sum of the first 15 multiples of 8.
Identify the AP formed by the multiples and use the sum formula.
Which term of the AP: 21, 18, 15, ... is -81?
Use the nth term formula and solve for n.
The sum of the first n terms of an AP is given by S_n = 4n - n^2. Find the first term and the common difference.
Find the first term by plugging n=1 into the sum formula, then find the second term and common difference.
Find the sum of the odd numbers between 0 and 50.
Identify the AP formed by the odd numbers and use the sum formula.
The 4th term of an AP is 0. Prove that the 25th term is triple the 11th term.
Express the 25th and 11th terms in terms of the common difference and compare them.
A man saves ₹100 in the first month, ₹150 in the second month, ₹200 in the third month, and so on. How much will he save in 2 years?
Identify the AP formed by the savings and use the sum formula for 24 terms.
Arithmetic Progressions - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Arithmetic Progressions to prepare for higher-weightage questions in Class X Mathematics.
Questions
Explain the concept of an Arithmetic Progression (AP) and how it differs from other sequences. Provide examples to illustrate your explanation.
Focus on the definition of AP and compare it with other sequences like geometric or harmonic progressions.
Find the 10th term of the AP: 3, 7, 11, 15, ... and explain the steps involved in the calculation.
Remember the formula for the nth term of an AP and ensure to substitute the correct values for a1, d, and n.
Compare the sum of the first n terms of an AP with the sum of the first n terms of a geometric progression (GP). Use examples to highlight the differences.
Focus on the formulas and how the common difference in AP and common ratio in GP affect the sum.
A ladder has rungs 25 cm apart. The lengths of the rungs decrease uniformly from 45 cm at the bottom to 25 cm at the top. If the distance between the top and bottom rung is 2.5 m, how many rungs does the ladder have?
Consider the distance between the first and last rung and how the rungs are spaced.
The sum of the first n terms of an AP is given by Sn = 3n^2 + 5n. Find the 10th term of the AP.
Use the relationship between the sum of terms and individual terms: an = Sn - Sn-1.
If the 5th term of an AP is 17 and the 9th term is 33, find the sum of the first 20 terms.
First find the common difference and first term, then apply the sum formula.
Explain why the sequence 1, 4, 9, 16, ... is not an AP. What type of sequence is it?
Check the difference between terms and identify the pattern of the sequence.
A contract specifies a penalty for delay of completion beyond a certain date: ₹200 for the first day, ₹250 for the second day, ₹300 for the third day, etc. How much penalty is paid for 30 days of delay?
Recognize the AP and use the sum formula with n=30.
The sum of the first 15 terms of an AP is 300 and the sum of the next 15 terms is 600. Find the first term and common difference.
Set up equations for S15 and S30, then solve the system of equations.
In an AP, the sum of the first 10 terms is 150 and the sum of the next 10 terms is 550. Find the AP.
Use the sum formulas for S10 and S20 to find a1 and d.
Arithmetic Progressions - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Arithmetic Progressions in Class X Mathematics.
Questions
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are 2.5 m apart, what is the length of the wood required for the rungs?
Consider the number of rungs and the arithmetic progression formed by their lengths.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP.
Express the third and seventh terms in terms of 'a' and 'd' and solve the given conditions.
Which term of the AP: 121, 117, 113, ..., is its first negative term?
Find the term where the expression for the nth term becomes less than zero.
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Set the sum of numbers before x equal to the sum after x and solve for x.
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the total volume of concrete required to build the terrace.
Calculate the volume of one step and multiply by the number of steps, considering if the dimensions change.
If the sum of the first n terms of an AP is given by Sn = 4n - n^2, find the first term and the common difference.
Use the given sum formula to find the first term and the difference between consecutive terms.
The sum of the first 16 terms of an AP is 112 and the sum of the next 14 terms is 518. Find the AP.
Set up equations for the sums of the specified terms and solve for 'a' and 'd'.
A man starts repaying a loan as a first installment of Rs. 100. If he increases the installment by Rs. 5 every month, what amount will he pay in the 30th installment?
Recognize the installments as an AP and use the formula for the nth term.
A spiral is made up of successive semicircles, with centers alternately at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ..., up to 13 semicircles. What is the total length of such a spiral?
Calculate the circumference of each semicircle and sum them up as an AP.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, and so on. What is the total distance the competitor has to run?
Consider the round trip for each potato and sum the distances as an AP.
Real Numbers encompass all rational and irrational numbers, forming a complete and continuous number line essential for various mathematical concepts.
Explore the world of Polynomials, understanding their types, degrees, and operations to solve algebraic expressions and equations effectively.
Explore the methods to solve a pair of linear equations in two variables, including graphical, substitution, elimination, and cross-multiplication techniques.
Explore the world of quadratic equations, learning to solve them using various methods like factoring, completing the square, and the quadratic formula.
