Arithmetic Progressions — Previous Year Questions (Class 10 Mathematics)
Arithmetic Progressions (AP) test understanding of common difference, nth term, and sum formulas. CBSE exams commonly ask for finding missing terms, derivi
TL;DR: Arithmetic Progressions (AP) test understanding of common difference, nth term, and sum formulas. CBSE exams commonly ask for finding missing terms, d…
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Arithmetic Progressions (AP) test understanding of common difference, nth term, and sum formulas. CBSE exams commonly ask for finding missing terms, derivi
Arithmetic Progressions — Previous Year Questions with Solutions
Q (2023, 1 mark): Find the 15th term of the AP: 2, 5, 8, 11, ...
Answer: Given AP: 2, 5, 8, 11, ...
First term a = 2
Common difference d = 5 - 2 = 3
nth term formula: a_n = a + (n-1)d
a_15 = 2 + (15-1)(3) = 2 + 14(3) = 2 + 42 = 44
Final Answer: 44
Q (2022, 3 marks): How many two-digit multiples of 3 are there?
Answer: Two-digit multiples of 3: 12, 15, 18, ..., 99
This is an AP with a = 12, d = 3, last term l = 99
Using a_n = a + (n-1)d:
99 = 12 + (n-1)(3)
99 - 12 = 3(n-1)
87 = 3(n-1)
n - 1 = 29
n = 30
Final Answer: 30 two-digit multiples of 3
Q (2021, 3 marks): The sum of the first n terms of an AP is 3n^2 + 2n. Find the 10th term.
Answer: S_n = 3n^2 + 2n
a_n = S_n - S_(n-1)
a_10 = S_10 - S_9
S_10 = 3(10)^2 + 2(10) = 300 + 20 = 320
S_9 = 3(9)^2 + 2(9) = 243 + 18 = 261
a_10 = 320 - 261 = 59
Final Answer: 59
Q (2023, 5 marks): If the mth term of an AP is 1/n and the nth term is 1/m, find the (mn)th term.
Answer: Given: a_m = 1/n and a_n = 1/m
Using a_n = a + (n-1)d:
a + (m-1)d = 1/n ... (1)
a + (n-1)d = 1/m ... (2)
Subtract (2) from (1):
(m - n)d = 1/n - 1/m = (m - n)/(mn)
d = 1/(mn)
From (1): a = 1/n - (m-1) × 1/(mn) = 1/n - (m-1)/(mn) = [m - (m-1)] / (mn) = 1/(mn)
a_mn = a + (mn-1)d = 1/(mn) + (mn-1) × 1/(mn) = [1 + mn - 1] / (mn) = mn / (mn) = 1
Final Answer: 1
Q (2022, 2 marks): The sum of first 12 terms of an AP is 168. If the 12th term is 23, find the first term.
Answer: S_n = n/2 [2a + (n-1)d] or S_n = n/2 (a + l)
For n = 12, l = 23:
S_12 = 12/2 (a + 23) = 168
6(a + 23) = 168
a + 23 = 28
a = 5
Final Answer: 5
Q (2021, 2 marks): Which term of the AP 5, 11, 17, 23, ... is 95?
Answer: AP: 5, 11, 17, 23, ...
a = 5, d = 6
Let 95 be the nth term:
95 = 5 + (n-1)(6)
90 = 6(n-1)
n - 1 = 15
n = 16
Final Answer: 16th term
Frequently Asked Questions
What is the difference between a series and a sequence?
A sequence is an ordered list of numbers (e.g., 2, 5, 8). A series is the sum of terms in a sequence (e.g., 2 + 5 + 8). An AP is a sequence; the sum of an AP is a series.
When should I use S_n = n/2 [2a + (n-1)d] vs S_n = n/2 (a + l)?
Use S_n = n/2 [2a + (n-1)d] when you know a, d, and n. Use S_n = n/2 (a + l) when you know the last term l. Both formulas are equivalent.
More Class 10 Mathematics PYQs
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