Question

Identify the 35th term of an arithmetic sequence where a1 = −7 and a18 = 95. (2 points)

203
197
168
163
Score: 2 of 2

Answer 1

To answer the problem, determine first the common difference by,

d = (a18 - a1) / (18 - 1)

d = ( 95 - -7) / (18 - 1) = 6

To solve for the 35th term

an = a1 + (n - 1)d

a35 = -7 + (35 - 1)6 = 197

Therefore, the 35th term is 197.

Answer 2

Option (b) is correct.

35th term of an arithmetic sequence is 197.

Explanation:

Given :
`a_1 =-7\ and\ a_(18)=95`

We have to find the 35 term of an arithmetic sequence whose
`a_1 =-7 \ and\ a_(18)=95`

For an Arithmetic sequence the general term is given as
`a_n=a+(n-1)d`,

where a is first term ,

n is number of term

d is common difference,

Thus, the 18th term
`a_(18)=a+(18-1)d`

We have
`a_(18)=95` , solving for d , we have,

`a_(18)=a+(18-1)d=95`

`95=a+17d`

Thus,
`\Rightarrow 95=-7+17d`

`\Rightarrow 95+7=17d`

`\Rightarrow 102=17d`

Divide both side by 17, we get,

`\Rightarrow d=6`

Now, 35th term of an arithmetic sequence is given by,

`\Rightarrow a_(35)=a+(35-1)d`

Substitute, a and d , we get,

`\Rightarrow a_(35)=-7+34(6)`

`\Rightarrow a_(35)=-7+204`

`\Rightarrow a_(35)=197`

Thus, 35th term of an arithmetic sequence is 197.

Option (b) is correct.