Question

Find S100 for the arithmetic sequence 4, 17, 30, ....

1295
64,750
129,900
1,295,000
none of these

Answer 1

There's a difference of 13 between consecutive terms in the sequence, so that the
`n`-th term of the sequence is

`a_n=4+13(n-1)=13n-9`

Then the sum of the first 100 terms of the sequence is

`S_(100)=\displaystyle\sum_(n=1)^(100)(13n-9)=13\sum_(n=1)^(100)n-9\sum_(n=1)^(100)1`

`S_(100)=13\frac{100\cdot101}2-9\cdot100`

`\boxed{S_(100)=64,750}`