Question

(CBSE 20131
13. Find the number of terms of the AP-12, -9, 6, ..., 21. If 1 is added to each term
of the AP, then find the sum of all terms of the AP thus obtained. (CBSE 20131​

Answer 1

Step-by-step explanation:

Here A = -12

d = -9-(-12) = 3

n =?

Now we know that An = A+(n-1)d

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

=> 21 = -12 +3n-3

=> 21 = -15+3n

=> 36 = 3n

=> n = 12

now also we know that sum of an ap

=> Sn = n/2[2a+(n-1)d]

=> Sn = 12/2[2(-12)+(12-1)3]

=> 6[-24+36-3]

=> 6(9)

=> 54

54 is the some of all the terms if we add one to every term then

=> -11,-8,-5

now

=> 12/2[2(-11)+(12-1)3)]

=> 6(-22+36-3)

=> 6(11)

=> 66 is the answer