Question

If `a_1=5` and `a_i = a_(i-1)+2`, what is the sum of the first 700 terms in the sequence?

Answer 1

Sum of first `n` terms is `492800`

Explanation:

In an arithmetic sequence whose first term is `a_1` and common difference, which is a term in the series "minus" preceding term, the sum of first `n` terms is given by

`S_n=n/2(2a_1+(n-1)d)`

Here as `a_i=a_(i-1)+2`, common difference `d=a_i-a_(i-1)=2` and `a_1=5`,

Hence, `S_700=700/2(2xx5+699xx2)`

= `350xx(10+1398)=350xx1408=492800`