Question

Find the sum to 100 terms of the series 1 + 4 + 7 + 5 + 13 + 6.........

• A. 7825
• B. 8825
• C. 9825
• D. 10825

Answer 1

The correct option is B

8825

The given series can be taken as two AP's by simple rearrangement of numbers, such as
(1 + 7 + 13......) and (4 + 5 + 6.......).

Now, we can find the sum of 50 terms for each AP formed. So, for first AP
$S_1=\frac{50}{2}(2+49\times 6)=7400$ and similarly,
$S_2=\frac{50}{2}(8+49\times 1)=1425$
So, Sum of first 100 terms $=7400+1425=8825$