Question

1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998

(a) Find the common difference d

(b) Find the value of n.​


pls help...

Answer 1

see explanation

Explanation:

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

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(b)

Given

`a_(n)` = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

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