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

##### 1 Answer

Feb 5, 2016

#### Answer:

3738

#### Explanation:

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

# S_n = n/2 [2a + (n-1)d ]# the common difference d , is required.

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

hence d = 9.

# rArr S_28 = 28/2 [(2xx12) + ( 27 xx 9) ]# = 14 ( 24

# +243) = 14 xx 267 = 3738 #