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Find the 16" term of the arithmetic sequence whose common difference is d= 8 and whose first term is a, = 1.

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Find the 16" term of the arithmetic sequence whose common difference is d= 8 and-example-1
User Hezekiah
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1 Answer

3 votes

Answer:


a_(16) = 121.

Explanation:

To go from the first term
a_(1) of this sequence to the second term
a_(2), add
d to
a_(1)\!.

To go from the first term
a_(1) of this sequence to the third term
a_(3), add
2\, d to
a_(1)\!.

In general, going from the first term
a_(1) of an arithmetic sequence to the
kth term, add
(k - 1)\, d to
a_(1)\!.

Thus, given an arithmetic sequence with
a_(1) as the first term and
d as the common difference, the
kth term of this sequence would be
a_(k) = a_(1) + (k - 1)\, d.

In this question,
a_(1) = 1 and
d = 8 for this arithmetic sequence. The
16th term of this sequence would be:


\begin{aligned}a_(16) &= 1 + (16 - 1) * 8 \\ &= 1 + 15 * 8 \\ &= 121\end{aligned}.

User Amrita
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