Question

Which sequences are geometric? Check all that apply. –2, –4, –6, –8, –10, … 16, –8, 4, –2, 1 –15, –18, –21.6, –25.92, –31.104, … 4, 10.5, 17, 23.5, 30, … 625, 125, 25, 5, 1, …

Answer 1

16, -8,4,-2,1
-15,-18, -21.6, -25.92, -31.104,...
625, 125, 25, 5, 1,...
these are the correct ones.

Answer 2

GIVEN :

The sequences are a) -2, -4, -6, -8, -10, …

b) 16, -8, 4, -2, 1

c) -15, -18, -21.6, -25.92,-31.104, …

d) 4, 10.5, 17, 23.5, 30, …

e)  625, 125, 25, 5, 1, …

TO FIND :

The sequence which are geometric sequence .

SOLUTION :

The three below sequences are geometric sequences

b) 16, -8, 4, -2, 1

c) -15, -18, -21.6, -25.92,-31.104, …

e)  625, 125, 25, 5, 1, …

FOR :

b) Given sequence is 16, -8, 4, -2, 1

Let $a_1=16$ ,$a_2=-8$ , $a_3=4$,...

The formula for common ratio is :

$r=\frac{a_2}{a_1}$

Substitute the values  $a_1=16$ ,$a_2=-8$ in the above  formula we get

$r=\frac{-8}{16}$

$=-\frac{1}{2}$

∴ $r=-\frac{1}{2}$

The formula for common ratio is :

$r=\frac{a_3}{a_2}$

Substitute the values  $a_3=4$ ,$a_2=-8$ in the above  formula we get

$r=\frac{4}{-8}$

$=-\frac{1}{2}$

∴ $r=-\frac{1}{2}$

Hence the common ratio $r=-\frac{1}{2}$

Hence the given sequence 16, -8, 4, -2, 1  is a geometric sequence.

c) Given sequence is -15, -18, -21.6, -25.92,-31.104,

Let $a_1=-15$ ,$a_2=-18$ , $a_3=-21.6$,...

The formula for common ratio is :

$r=\frac{a_2}{a_1}$

Substitute the values  $a_1=-15$ ,$a_2=-18$ in the above  formula we get

$r=\frac{-18}{-15}$

$=\frac{6}{5}$

∴ $r=1.2$

The formula for common ratio is :

$r=\frac{a_3}{a_2}$

Substitute the values  $a_3=-21.6$ ,$a_2=-18$ in the above  formula we get

$r=\frac{-21.6}{-18}$

∴ $r=1.2$

Hence the common ratio $r=1.2$

Hence the given sequence -15, -18, -21.6, -25.92,-31.104,   is a geometric sequence.

e) Given sequence is 625, 125, 25, 5, 1, …

Let $a_1=625$ ,$a_2=125$ , $a_3=25$,...

The formula for common ratio is :

$r=\frac{a_2}{a_1}$

Substitute the values  $a_1=625$ ,$a_2=125$ in the above  formula we get

$r=\frac{625}{125}$

$=\frac{1}{5}$

∴ $r=\frac{1}{5}$

The formula for common ratio is :

$r=\frac{a_3}{a_2}$

Substitute the values  $a_3=25$ ,$a_2=125$ in the above  formula we get

$r=\frac{25}{125}$

$=\frac{1}{5}$

∴ $r=\frac{1}{5}$

Hence the common ratio $r=\frac{1}{5}$

Hence the given sequence 625, 125, 25, 5, 1, … is a geometric sequence.

∴ The three below sequences are geometric sequences.

b) 16, -8, 4, -2, 1

c) -15, -18, -21.6, -25.92,-31.104, …

e)  625, 125, 25, 5, 1, …