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

Answer:

The sum of all terms of the A.P. thus obtained is 66 .

Step-by-step explanation:

Given :  

A.P. is -12, -9, -6,...…21

Here, a = -12, an = 21 and d = - 9 - (-12)  

d = - 9 + 12  

d = 3

 

By using the formula , nth term ,an = a + (n - 1)d

21 = -12 + (n -1) (3)

21 = - 12 + 3n - 3

21 = -15 + 3n

21 + 15 = 3n

36 = 3n

n = 36/3

n = 12

 

If 1 is added to each term than A.P. is  -11, - 8, - 5…...22

Here, a = -11, d = 3

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S12 = 12/2 [2(-11) + (12 -1) × 3]

S12 = 6 [-22 + 11 × 3]

S12 = 6 [- 22 + 33]

S12 = 6 × 11

S12 = 66

Hence, the sum of all terms of the A.P. thus obtained is 66 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

answers are 12 terms and sum is 66