Question

Need help with knowing how to do this

Answer 1

see explanation

Explanation:

(a)

The common difference (d) in an arithmetic sequence is

d =
`a_(2)` -
`a_(1)` = 24 - 2 = 22

To obtain the next term in the sequence add 22 to the previous term

`a_(4)` = 46 + 22 = 68

`a_(5)` = 68 + 22 = 90

`a_(6)` = 90 + 22 = 112

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(b)

The n th term of an arithmetic sequence is

`a_(n)` = a + (n - 1)d

where a is the first term and d the common difference

here a = 2 and d = 22, hence

`a_(n)` = 2 + 22(n - 1) = 2 + 22n - 22 = 22n - 20 ← n th term formula

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(c)

Using the n th term formula

`a_(35)` = (22 × 35) - 20 = 770 - 20 = 750