What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms?

Feb 19, 2016

1848

Explanation:

The sum to n terms of an arithmetic sequence is found by using

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

where a , is the first term and d , the common difference

here a = 8 and d = 14 - 8 = 20 - 14 =.......= 6

hence ${S}_{24} = \frac{24}{2} \left[\left(2 \times 8\right) + \left(23 \times 6\right)\right]$

= 12[ 16 + 138 ] = 12( 154) = 1848