Question

Given two terms in a geometric sequence find the first five terms.

Answer 1

The first five terms of the geometric series is : -2, -6, -18, -54, -162.

To solve the given problem :

Given :  $a_{5} = -162$

$a_{2} = -6$

We know G.P. series always increases in the form $a.r^{n-1}$

Similarly, $a_{5} = a.r^{5-1} = a.r^{4} = -162$

$a_{2} = a.r^{2-1} = a.r = -6$

Now, $\frac{a_{5} }{a_{2} } = \frac{a.r^{4} }{a.r^{1} } = r^{4-1}$

$r^{3} = \frac{-162}{-6} = 27$

$r = \sqrt[3]{27} = 3$

Now,

$a_{2} = a.r = -6\\a.(3) = -6\\a = -2$

The first 5 terms are  :  $a, a.r, a.r^{2} , a.r^{3} , a.r^{4}$

$-2 , (-2).3 , (-2).3^{2} , (-2).3^{3} , (-2).3^{4}$

Therefore, The first 5 terms are  : -2, -6, -18, -54, -162.

To learn more about G.P. series, refer to :

brainly.com/question/24643676

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