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

Polynomial arithmetic
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asked 2021-01-02
Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7.

## Answers (1)

2021-01-03
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.
$$\displaystyle{a}_{{{8}}}={4}+{\left({8}-{1}\right)}{\left(-{7}\right)}$$
$$\displaystyle{a}_{{{8}}}={4}+{7}{\left(-{7}\right)}$$
$$\displaystyle{a}_{{{8}}}={4}-{49}$$
$$\displaystyle{a}_{{{8}}}=-{45}$$

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