How many terms are there in 20, 25, 30, ......, 140?
2023
How many terms are there in 20, 25, 30, ......, 140?
Answer: B. 25 — In an arithmetic progression (AP), consecutive terms differ by a constant amount called the common difference. If a is the first term, d is the common…
- A.
22
- B.
25
- C.
23
- D.
78
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Correct answer: B
In an arithmetic progression (AP), consecutive terms differ by a constant amount called the common difference. If a is the first term, d is the common difference, and l is the last (nth) term, the number of terms n satisfies l = a + (n − 1)d. This relation lets us find n directly whenever a, d, and l are known.
Identify the given quantities for this progression: first term a = 20, common difference d = 25 − 20 = 5, and last term l = 140.
Substitute these values into l = a + (n − 1)d: 140 = 20 + (n − 1) × 5.
Isolate (n − 1): (n − 1) = (140 − 20) / 5 = 120 / 5 = 24.
Solve for n: n = 24 + 1 = 25.
To verify, compute the 25th term directly: a + (25 − 1)d = 20 + 24 × 5 = 20 + 120 = 140, which matches the given last term, confirming the count.
Hence, the progression 20, 25, 30, ……, 140 has 25 terms.