Question

Find S20 of the series whose first terms are: 30, 22, 14, 6, ...

Answer 1

Answer:

- 920

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = 22- 30 = 14 - 22 = 6 - 14 = - 8

This indicates the sequence is arithmetic with sum to n terms given by

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 30 and d = - 8 , thus

$S_{20}$ = $\frac{20}{2}$ [ (2 × 30) + (19 × - 8) ]

     = 10(60 - 152)

     = 10 × - 92

     = - 920