Question

MU 3. Use the sequence below to complete each task. 3, 11, 19, 27, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 24th term (224)

Answer 1

This is an arithmetic progression.

The common difference is 8:

$11-3=8,19-11=8,\ldots.$

The equation will be derived from the arithmetic progression:

$a_n=a+(n-1)d$$a_n=3+(n-1)\cdot8\Rightarrow a_n=3+8n-8\Rightarrow a_n=-5+8n_{}$

To find the 24th element:

$a_{24}=-5+8\cdot(24)\Rightarrow a_{24}=-5+192\Rightarrow a_{24}=187$