Question

Sum of the first term in an AP is 6 and that of the last three term is
16. If the AP has 13 term what it's the
Sum of middle three terms?​

Answer 1

Answer:

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

I explained briefly and quickly, so if any doubt is popping in your mind. Ask me in comment section. If Any mistake made by me in calculations plz inform.