The number of terms in the sequence 20, 25, 30, ....., 160 is:

Concept

A list of numbers with a constant common difference between consecutive terms is an arithmetic progression (AP). 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. This works because each step of size d moves from one term to the next, so (l − a)/d counts the number of steps, and adding 1 includes the starting term itself.

Application

1. Identify the parameters: first term a = 20, last term l = 160, and common difference d = 25 − 20 = 5.

2. Count the steps from first to last: (l − a)/d = (160 − 20)/5 = 140/5 = 28.

3. Add 1 to include the first term: n = 28 + 1 = 29.

Cross-check

Verify with the nth-term formula a + (n − 1)d. Substituting n = 29 gives 20 + (29 − 1)×5 = 20 + 28×5 = 20 + 140 = 160, which is exactly the stated last term. So the sequence has 29 terms.