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2 years ago

Find the sum of the first 90 terms of the sequence -4,-1,2,5,8

Mathematics

1 answer:

telo118 [61]2 years ago

4 0

Answer:

1655

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

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

Here a₁ = - 4, d = 3 and n = 90, thus

$S_{90}$ = $\frac{90}{2}$ [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655

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