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2 years ago

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

Mathematics

1 answer:

Alona [7]2 years ago

4 0

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

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