Question

Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .

Answer 1

the pattern doubles, .75 x 2= 1.5. 1.5 x 2= 3, and so on. so the answer would be 1,536

Answer 2

Answer:

1536

Step-by-step explanation:

Given : A geometric sequence 0.75, 1.5, 3, 6, . . .

To Find:Find the 12th term

Solution:

0.75, 1.5, 3, 6, . . .

First term =a = 0.75

Common difference = $r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2$

nth term of G.P. = $a_n=a r^{n-1}$

Where a = First term = 0.75

r = common difference = 2

Substitute n = 12

$a_{12}= 0.75 (2)^{12-1}$

$a_{12}= 0.75 (2)^{11}$

$a_{12}= 1536$

Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.