# What is the sum of a 28–term arithmetic sequence where the first term is 12 and the last term is 255?

Feb 5, 2016

3738

#### Explanation:

To calculate the 'sum to n terms' of an arithmetic sequence use:

${S}_{n} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]$

the common difference d , is required.

28th term = a + (n-1)d = 12 +27d =255 , hence 27d = 243

hence d = 9.

$\Rightarrow {S}_{28} = \frac{28}{2} \left[\left(2 \times 12\right) + \left(27 \times 9\right)\right]$

= 14 ( 24 +243) = 14 xx 267 = 3738