Question

The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence? 1. an = 8n + 10 2. an = 8n − 14 3. an = 16n + 10 4. an = 16n − 38

Answer 1

The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence?
1. an = 8n + 10
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆ 2. an = 8n − 14
3. an = 16n + 10
4. an = 16n − 38

Answer 2

Option 2nd is correct

`a_n =8n-14`

Explanation:

The nth term for the arithmetic equation is give by:

`a_n = a_1+(n-1)d` ....[A]

where,

`a_1` is the first term

d is the common difference and

n is the number of term.

As per the statement:

The fourth term in an arithmetic sequence is 18 and the seventh term is 42

⇒
`a_4 = 18` and
`a_7 = 42`

then by above definition we have;

`a_1+3d = 18` .....[1]

`a_1+6d = 42` .....[2]

Subtract equation [1] from [2] we have;

3d = 24

Divide both sides by 3 we have;

d = 8

Substitute in [1] we have;

`a_1+24 = 18`

Subtract 24 from both sides we have;

`a_1=-6`

We have to find the equation for the nth term of this sequence

Substitute the given values in [A] we have;

`a_n = -6+(n-1)\cdot 8`

⇒
`a_n = -6+8n-8`

⇒
`a_n =8n-14`

Therefore, an equation for the nth term of this sequence is,
`a_n =8n-14`