Question

Find the number of terms of the AP -12, -9, -6, .., 21. If 1 is added to each term of this AP then 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 = 2 l

Suppose there are n terms in the AP.

∴ l= a_n = 21 

⇒ -12 + (n-1) × 3 = 21           [a_n  = a +(n-1) d]

⇒ 3n - 15 = 21

⇒ 3n = 21 +15 = 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
∴ Sum of the terms of this AP

`= 12/2 (-11+22)         [ S_n = n/2 (a+l) ]`

= 6 × 11

=66 

Hence, the required sum is 66.