Write the first six terms of the arithmetic sequence a_{n}=a_{n-1}+4, a_{1}=-7

Question
Polynomial arithmetic
asked 2020-11-08
Write the first six terms of the arithmetic sequence \(\displaystyle{a}_{{{n}}}={a}_{{{n}-{1}}}+{4},{a}_{{{1}}}=-{7}\)

Answers (1)

2020-11-09
Step 1
Given:
\(\displaystyle{a}_{{{1}}}=-{7},{a}_{{{n}}}={a}_{{{n}-{1}}}+{4}\)
To find first six terms.
Step 2
From
\(\displaystyle{a}_{{{n}}}={a}_{{{n}-{1}}}+{4},\ {a}_{{{1}}}=-{7}\) and \(\displaystyle{n}={2},\ {3},\ {4},\ {5}\)
we get
\(\displaystyle{a}_{{{2}}}={a}_{{{1}}}+{4}\)
\(\displaystyle=-{7}+{4}\)
\(\displaystyle=-{3}\)
\(\displaystyle{a}_{{{3}}}={1}\)
\(\displaystyle{a}_{{{4}}}={5}\)
\(\displaystyle{a}_{{{5}}}={9}\)
\(\displaystyle{a}_{{{6}}}={13}.\)
Therefore first six terms are \(\displaystyle-{7},\ -{3},\ {1},\ {5},\ {9},\ {13}.\)
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