How do you find the term n=20, given the arithmetic sequence $a_{1} = - 4$ $a_1=-4$ and d=-9?

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Answer 1 · 2018-06-13T18:51:27

$a_{20} = - 175$ $a_20=-175$ . See below

An arithmetic sequence has the general term given by

$a_{n} = a_{1} + (n - 1) d$ $a_n=a_1+(n-1)d$

Then applying given values

$a_{n} = - 4 + (n - 1) (- 9) = - 4 - 9 n + 9 = - 9 n + 5$ $a_n=-4+(n-1)(-9)=-4-9n+9=-9n+5$

For $n = 20$ $n=20$ , we have $a_{20} = - 9 \cdot 20 + 5 = - 175$ $a_20=-9·20+5=-175$

How do you find the term n=20, given the arithmetic sequence a1=−4a_1=-4 and d=-9?