Rivka Thorpe

## Answered question

2020-12-03

1. Is the sequence $0.3,1.2,2.1,3,...$ arithmetic? If so find the common difference.
2. An arithmetic sequence has the first term ${a}_{1}=-4$ and common difference $d=-\frac{4}{3}$. What is the ${6}^{th}$ term?
3. Write a recursive formula for the arithmetic sequence $-2,-\frac{7}{2},-5,-\frac{13}{2}...$ and then find the ${22}^{nd}$ term.
4. Write an explicit formula for the arithmetic sequence $15.6,15,14.4,13.8,...$ and then find the ${32}^{nd}$ term.
5. Is the sequence $-2,-1,-\frac{1}{2},-\frac{1}{4},...$ geometric? If so find the common ratio. If not, explain why.

### Answer & Explanation

Bella

Skilled2020-12-04Added 81 answers

Step 1
Given:
${a}_{1}=-4$
$d=-\frac{4}{3}$
${a}^{6}=?$
Step 2
We know in A.P
${t}_{n}=a+\left(n-1\right)d$
Where a is the first term, d the common difference
${t}_{6}=-4+\left(6-1\right)\left(-\frac{4}{3}\right)$
$=-4+\left(5\right)\left(-\frac{4}{3}\right)$
$=-4-\frac{20}{3}$
$=\frac{-12-20}{3}$
$=\frac{-32}{3}$

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