Question

Q.2] Solve the following:
A] Find t, for the A.P. 12,9,6,....​

Answer 1

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


Given AP is -12, -9, -6, ..., 21
First term, a = -12
Common difference, d = 3
Let 21 be the nth term of the A.P.
21 = a + (n - 1)d
21 = -12 + (n - 1) 3
33 = (n - 1) 3
n = 12
Sum of the terms of the AP = S12
=
If 1 is added to each term of the AP, the sum of all the terms of the new AP will increase by n, i.e., 12.
Sum of all the terms of the new AP = 54 + 12 = 66