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

find a formula for an for the arithmetic sequence. $$\displaystyle{a}_{{1}}=-{4},{a}_{{5}}={16}$$

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Nathalie Redfern

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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