Question

20 arithmetic means are inserted between 2 and 100. The sum of all 20 arithmetic means is

• A. 1000
• B. 510
• C. 1020
• D. 500

Answer 1

The correct option is C 1020

Let $A_1,A_2,A_3,A_4,,....,A_{20}$be the arithmetic means inserted between 2 and 100 and d be the common difference of the AP thus formed $2,A_1,A_2,A_3,A_4,,....,A_{20},100$
We know that in an AP sum of terms equidistant from median(the term(s) which is(are) at center) is same.
$A_1+A_{20}=2+100=102A_1+A_2+A_3+,....+A_{20}=\frac{20}{2}\left(A_1+A_{20}\right)=10\times 102=1020$