Question

The first term of an arithmetic sequence is 14. The 25th term is 206. find the common difference

Answer 1

We can manipulate the arithmetic sequence formula to solve this problem.

Let's look at
`a_(n) = a_(1) +(n-1)d` where
`a_(n)` is the
`n^(th)` term,
`a_(1)` is the first term,
`n` is the number of terms, and
`d` is the common difference. We already know that
`a_(1)` is equal to
`14`,
`n` is equal to
`25`, and
`a_(25)` is equal to
`206`. This therefore leave us with only the common difference to solve.

Manipulating the formula we can arrive at the answer:

`206 = 14 +(25-1)d`

`192 = (24)d`

`d=8`

ANSWER: The common difference is 8.