Question

Find S12 for an arithmetic sequence with a1 = 8 and a5 = 28.

180
360
426
852
none of these

Answer 1

The
`n`-th term of the sequence is

`a_n=8+d(n-1)`

where
`d` is the common difference between consecutive terms.

Since
`a_5=28`, we have

`28=8+4d\implies d=5`

so that

`a_n=8+5(n-1)=5n+3`

Then the sum of the first 12 terms of the sequence is

`S_(12)=\displaystyle\sum_(n=1)^(12)(5n+3)=5\sum_(n=1)^(12)n+3\sum_(n=1)^(12)1`

`S_(12)=5\frac{12\cdot13}2+3\cdot12`

`\boxed{S_(12)=426}`