Answer
The given sequence = 1, -2, 4, -8, 16,.....................
$\frac{a_{2}}{a_{1}}$ = $\frac{-2}{1}$ = -2
$\frac{a_{3}}{a_{2}}$ = $\frac{4}{-2}$ = -2
$\frac{a_{4}}{a_{3}}$ = $\frac{-8}{4}$ = -2
$\frac{a_{5}}{a_{4}}$ = $\frac{16}{-8}$ = -2
From above we observe that $\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = $\frac{a_{5}}{a_{4}}$ = -2 .
When the ratio of two consecutive terms of sequence is constant then the sequence is said to be a geometric sequence or geometric procession.
Work Step by Step
The given sequence = 1, -2, 4, -8, 16,.....................
$\frac{a_{2}}{a_{1}}$ = $\frac{-2}{1}$ = -2
$\frac{a_{3}}{a_{2}}$ = $\frac{4}{-2}$ = -2
$\frac{a_{4}}{a_{3}}$ = $\frac{-8}{4}$ = -2
$\frac{a_{5}}{a_{4}}$ = $\frac{16}{-8}$ = -2
From above we observe that $\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = $\frac{a_{5}}{a_{4}}$ = -2 .
When the ratio of two consecutive terms of sequence is constant then the sequence is said to be a geometric sequence or geometric procession.
