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

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2 votes
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.
User Daniel Khoroshko
by
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