Question

Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7.

Answer 1

Step 1
we have to find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7.
Step 2
Let the eighth term is denoted by \(\displaystyle{a}_{{{8}}}\)
here
\(\displaystyle{a}_{{{1}}}=\) first term \(\displaystyle={4}\)
\(\displaystyle{d}=-{7}\)
now as we know that \(\displaystyle{n}^{{{t}{h}}}\) term is given as
\(\displaystyle{a}_{{{n}}}={a}_{{{1}}}+{\left({n}-{1}\right)}{d}\)
where \(\displaystyle{a}_{{{1}}}\) is the first term an d is the common difference.
\(\displaystyle{a}_{{{8}}}={4}+{\left({8}-{1}\right)}{\left(-{7}\right)}\)
\(\displaystyle{a}_{{{8}}}={4}+{7}{\left(-{7}\right)}\)
\(\displaystyle{a}_{{{8}}}={4}-{49}\)
\(\displaystyle{a}_{{{8}}}=-{45}\)