The number of terms in the sequence 20, 25, 30, ............., 150 is:

Concept

In an arithmetic progression (AP) the terms increase by a fixed common difference. If the first term is a, the common difference is d, and the last term is L, the count of terms is given by the identity n = (L − a) / d + 1. The "+ 1" is essential: it counts the first term itself, not just the gaps between terms.

Application

Here the sequence is 20, 25, 30, …, 150.

1. Identify the first term: a = 20.

2. Find the common difference: d = 25 − 20 = 5.

3. Identify the last term: L = 150.

4. Count the gaps: (L − a) / d = (150 − 20) / 5 = 130 / 5 = 26.

5. Add 1 to include the first term: 26 + 1 = 27.

So the sequence has 27 terms.

Cross-check

Use the nth-term formula in reverse: the n-th term is a + (n − 1)·d. Setting this equal to 150 gives 20 + (n − 1)·5 = 150, so (n − 1)·5 = 130, hence n − 1 = 26 and n = 27. Both methods agree.