Answer
The given $n^{th}$ term ( $a_{n}$) = $3.5^{n}$
$\frac{a_{2}}{a_{1}}$ = $\frac{12.25}{3.5}$ = 3.5
$\frac{a_{3}}{a_{2}}$ = $\frac{42.875}{12.25}$ = 3.5
$\frac{a_{4}}{a_{3}}$ = $\frac{150.0625}{42.875}$ = 3.5
$\frac{a_{5}}{a_{4}}$ = $\frac{525.21875}{150.0625}$ = 3.5
From this we observe that
$\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = $\frac{a_{5}}{a_{4}}$ = 3.5
Here each term after the first term is found by multiplying the previous one by a fixed, non-zero number called the common ratio = 3.5.
Work Step by Step
The given $n^{th}$ term ( $a_{n}$) = $3.5^{n}$
$a_{1}$ = $3.5^{1}$ = 3.5
$a_{2}$ = $3.5^{2}$ = 12.25
$a_{3}$ = $3.5^{3}$ = 42.875
$a_{4}$ = $3.5^{4}$ = 150.0625
$a_{5}$ = $3.5^{5}$ = 525. 21875
$\frac{a_{2}}{a_{1}}$ = $\frac{12.25}{3.5}$ = 3.5
$\frac{a_{3}}{a_{2}}$ = $\frac{42.875}{12.25}$ = 3.5
$\frac{a_{4}}{a_{3}}$ = $\frac{150.0625}{42.875}$ = 3.5
$\frac{a_{5}}{a_{4}}$ = $\frac{525.21875}{150.0625}$ = 3.5
From this we observe that
$\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = $\frac{a_{5}}{a_{4}}$ = 3.5
Here each term after the first term is found by multiplying the previous one by a fixed, non-zero number called the common ratio = 3.5.
