Question

3, 9, 15,.

Find the 45th term.

Answer 1

Given the first three terms of the sequence to be

`3,9,15,...`

It is observed that each successive term of the sequence is obtained by the addition of 6 to the preceding term.

Thus, the sequence is an arithmetic sequence.

The nth term of an arithmetic sequence is given as

`a_n=ar^(r-1)`

Thus, from the given sequence,

`a=3`

`d=9-3=6 \ \text{OR} \ 15-9=6`

`n=45`

`T_(45) \ \text{is thus evaluated as}`

`T_(45)=3+(45-1)6`

`T_(45)=3+(44*6)`

`T_(45)=3+264`

`T_(45)=267`

The 45th term of the sequence is thus 267

Answer 2

a=3 d=6 n=45

A45= 3+44×6=267

Explanation:

i hope you find it helpful