How do you write a rule for the nth term of the arithmetic sequence and then find a_22 given 5/8, 5/4, 15/8, 5/2,...?

Feb 19, 2017

If we write everything with $8$ as a denominator it's easier:

Explanation:

$\frac{5}{8} , \frac{10}{8} , \frac{15}{8} , \frac{20}{8.} . .$

So apparently the formula is ${a}_{n} = \frac{5 \times n}{8}$

So ${a}_{22} = \frac{5 \times 22}{8} = \frac{110}{8}$

Which can also be written as ${a}_{22} = \frac{55}{4} \mathmr{and} 13 \frac{3}{4}$ as you wish.