Class 10 nth Term of an AP — practice questions with answers
Algebra — Sequences · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. For an AP, the nth term is given by a_n = a + (n - 1)d. What does 'd' represent here?
AThe first term
BThe common difference
CThe number of terms
DThe last term
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Answer: B) The common difference
In a_n = a + (n - 1)d, 'a' is the first term and 'd' is the common difference (the fixed gap between consecutive terms).
2. The nth term of an AP is a_n = 5 - 2n. Find the 10th term.
A-14
B-30
C-16
D-15
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Answer: D) -15
a_10 = 5 - 2*10 = 5 - 20 = -15.
3. A potato race: a bucket is placed at the start, and potatoes are 5 m, 8 m, 11 m, ... from it (an AP). A player runs from the bucket to a potato and back, one potato at a time.
How far does the player run for the 10th potato alone (there and back)?
A128
B64
C58
D70
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Answer: B) 64
Distance to 10th potato: a = 5, d = 3 => a_10 = 5 + 9*3 = 32 m. There and back = 2*32 = 64 m.
4. An AP has 40 terms. Its 40th term is 122 and its common difference is 3. Find its 33rd term.
A98
B101
C104
D143
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Answer: B) 101
Going back from the 40th term to the 33rd term is 7 steps, so a_33 = a_40 - 7d = 122 - 21 = 101. Adding instead of subtracting gives 143; using 8 steps gives 98 and using 6 steps gives 104.
5. The sum of the 3rd and 7th terms of an AP is 6, and their product is 8. Given that the AP is increasing, find its first term.
A1
B2
C0.5
D4
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Answer: A) 1
Two numbers with sum 6 and product 8 are 2 and 4. Since the AP increases, a_3 = 2 and a_7 = 4. Then a_7 - a_3 = 4d = 2, so d = 0.5, and a = a_3 - 2d = 2 - 1 = 1. The value 2 is the 3rd term mistaken for the first, 4 is the 7th term, and 0.5 is the common difference.