Question

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

Answer 1

Sol:

Given A.P. = -12, -9, -6,... 21

First term (a) = - 12

Common difference = (-9) - (-12) = -9 + 12 = 3

Last term = 21

n value of the last term of the A.P. gives the number of terms of the A.P.

a + (n - 1)d = 21
-12 + (n - 1)(3) = 21
-12 + 3n - 3 = 21
3n - 15 = 21
3n = 21 + 15
3n = 36
n = 36/3
n = 12

So, the number of terms of the A.P. is 12

If 1 is added to each of the terms of the A.P.

-11, -8, -5, -2 .......... 22

Sum of the terms of the A.P.= 12/2 [(-11) + (22)]
= 66.