How many terms are there in the AP 9, 16, 23, 30……………282?

Given the Arithmetic Progression (AP) 9, 16, 23, 30, ..., 282, we are tasked with finding how many terms are there in the AP.

Here, we know that:

• First term (a) = 9
• Common difference (d) = 16 - 9 = 7

We are asked to find the number of terms, n, in the given AP, where the last term (Tn) is 282. The formula for the n^th term of an AP is:

Tn = a + (n – 1) × d

Substitute the known values:

282 = 9 + (n – 1) × 7

Now, solve for n:

282 = 9 + 7n – 7

282 = 7n + 2

282 – 2 = 7n

280 = 7n

n = 280 / 7

n = 40

Thus, the given AP has 40 terms.

The correct answer is c) 40.