Question

Given a term in an arithmetic sequence and

the common difference find the 100th term.


a14= 102
d = 10


Please help, i’m struggling.

Answer 1

100th term = 962

Explanation:

You need to find the first term of the sequence

The formula to use is

`a_(n) = a_(1) + (n - 1)d` In your problem, n = 14. So,

`102 = a_(1) + (14 - 1)10\\102 = a_(1) + 130\\a_(1) = -28\\\\`

Now you can find the 100th term. n = 100, first term = -28 and d = 10

`a_(100) = -28 + (100 - 1)10\\ = -28 + 990\\ = 962`

100th term = 962