Question

Find the first term in the arithmetic sequence?

$\_,8\frac{1}{3},7,5\frac{2}{3},4\frac{1}{3},\mathrm{...}$

1. 3
2. $9\frac{2}{3}$
3. $10\frac{1}{3}$
4. 11

Short answer

B) The first term in the arithmetic sequence is$9\frac{2}{3}$.

Step-by-step solution

Step 1. Given Information.

The given arithmetic sequence is $\_\_,8\frac{1}{3},7,5\frac{2}{3},4\frac{1}{3},\mathrm{...}$

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $7-8\frac{1}{3}=-1\frac{1}{3}$

The difference between the next two terms is $5\frac{2}{3}-7=-1\frac{1}{3}$

So, the common difference is $-1\frac{1}{3}$.

The first term is given by:

$\begin{array}{l}{a}_1-1\frac{1}{3}=8\frac{1}{3}\\ a_1=8\frac{1}{3}+1\frac{1}{3}\\ a_1=9\frac{2}{3}\end{array}$

Step 3. Conclusion.

Hence, the first term in the arithmetic sequence is$9\frac{2}{3}$ .