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 \(\displaystyle-{7},\ -{3},\ {1},\ {5},\ {9},\ {13}.\)

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 \(\displaystyle-{7},\ -{3},\ {1},\ {5},\ {9},\ {13}.\)