Question

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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Answer 1

`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
`k`th 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
`k`th 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
`16`th term of this sequence would be:

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