Question

Find the number of termsof the AP - 12, -9, -6, ..., 21. If 1 is added to each term of tthis AP then find the sum of all terms of the AP thus obtained.

Answer 1

The given AP is -12, -9, -6,…….., 21.

Here, a = -12, d = -9 – (-12) = -9 + 12 = 3 and l = 21

Suppose there are n terms in the AP.

Therefore,
⇒−12+(n–1)×3=21
⇒3n–15=21
⇒3n=36
⇒n=12

Thus, there are 12 terms in the AP.

If 1 is added to each term of the AP, then the new AP so obtained is -11, -8, -5, ....., 22.

Here, first term, A = -11, last term, L = 22 and n = 12

Therefore, Sum of the terms of this AP

=(n/2)(2A+(n-1)d)

= 66

Hence, the required sum is 66.