find a formula for an for the arithmetic sequence. a_1 = -4, a_5 = 16

snowlovelydayM 2021-09-15 Answered
find a formula for an for the arithmetic sequence. \(\displaystyle{a}_{{1}}=-{4},{a}_{{5}}={16}\)

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Expert Answer

Nathalie Redfern
Answered 2021-09-16 Author has 6420 answers

Generic formula for an arithmetic sequence in which nth term equals the first term plus the common difference times the number of differences between the first term and the nth term:
\(\displaystyle{a}_{{n}}={a}_{{1}}+{d}{\left({n}-{1}\right)}\), then
1) \(\displaystyle{a}_{{5}}={a}_{{1}}+{4}_{{d}}\)
\(\displaystyle{16}=-{4}+{4}_{{d}}\)
\(\displaystyle{d}={5}\)
2) \(\displaystyle{a}_{{n}}=-{4}+{5}{\left({n}–{1}\right)}\)
\(\displaystyle{a}_{{n}}=-{4}+{5}_{{n}}–{5}={5}_{{n}}-{9}\)

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