Question

the third term of an arithmetic sequence is 24 and the fifth is 32 if the first term is a1. which is an equation nth term of the sequence

Answer 1

an = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
24, ____, 32
a3 a4 a5
Subtract 32-24 = 8
Subtract a5 - a3 = 2
Divide 8/2 = 4
d = 4
Use d and one of the values they give us to find a1.
a3 = 24
24 = a1 + (3 - 1)(4)
24 = a1 + 2(4)
24 = a1 + 8
Subtract 8 from both sides
16 = a1
an = 16 + (n - 1)(4)
Can also be written
an = 16 + 4n - 4
an = 4n + 12

Answer 2

The nth term of the sequence is
`a_n=4n+12`

Explanation:

Given:
`a_3=24,\ \ a_5=32`

First term:
`a_1`

Formula:

`a_n=a_1+(n-1)d`

where, d is common difference

`a_3=24`

`a_1+2d=24`

`a_1+4d=32`

Subtract both equation

`2d=32-24`

`2d=8`

`d=4`

Put d=4 into
`a_1+2d=24`

`a_1+2(4)=24`

`a_1=16`

Now, we will find nth term of the sequence.

`a_n=16+(n-1)4`

`a_n=16+4n-4`

`a_n=4n+12`

Hence, The nth term of the sequence is
`a_n=4n+12`