Question

what should be the answer to this question​

Answer 1

Step-by-step explanation:

Given :- a = -12 and a6 = 8

so, An = a + (n-1) d

A6 = -12 + (6-1) d

8 = -12 + (5)d

8 + 12 = 5d

20 = 5d

20/5 = d

4 = d

Hence, our AP is -12, -8, -4, 0, ...

Now, Sn = n/2 {2a + (n-1) d}

120 = n/2 { 2x(-12) + (n-1) 4 }

120 = n/2 { -24 + 4n - 4 }

120 = n/2 { -28 + 4n }

120 = n { -14 + 2n } (:- divided by 2)

120 = -14n + 2n^2

2n^2 - 14n - 120 = 0

n^2 - 7n - 60 = 0 (:- divided by 2)

n^2 - 12n + 5n - 60 = 0

n ( n - 12) + 5 ( n - 12) = 0

( n - 12) or ( n + 5) = 0

n = 12 or n = -5

Here, we will not consider negative terms.

So, the total number of terms are 12.

I hope it will help you.