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

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

= [ 2a₁ + (n - 1)d ]

Here a₁ = - 4, d = 3 and n = 90, thus

= [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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