Question

The sum of the first 3 terms in an AP is 6 and that of the last 3 is 16. If the AP has 13 terms, what is the sum of the middle three terms? A. 7 B. 9 C. 11 D. 13

Answer 1

Answer:

The answer should be Option C. 11

Step-by-step explanation:

The some part of explanation is given as attachment.

Here, a= 11/3 and d=1/3

(continued....)

Sum of 3 middle terms = (a-d) +a+(a+d)

= 3a

=3(11/3)

=11

Thus, the answer is 11.

Hope this helped you.

Thank you.

Answer 2

Answer:

(c). 11

Step-by-step explanation:

let first term be a. And common difference is d.

So given a+a+d+a+2d=6

3(a+d) =6

==>|a+d=2

Given that a+12d+a+11d+a+10d=16

3a+33d=16

==> 3(2-d) +33d=16

6+30d=16

==>| d=1/3

Now a=2-1/3 = 5/3

Let's see what are middle terms,

Since no of terms =13.

Middle most term =(13+1) /2 th term.

That is 7th term == a+6d

Now middle 3 terms are

a+5d, a+6d, a+7d

Sum of them = 3a+18d

==>sum of middle 3 terms= 5+6= 11