Find the first 5 terms of the geometric progression if the common ratio is -4 and the 4th term is 16.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The consecutive terms of a GP have a common ratio. Let the common ratio be r and let the first term be a.

The nth term of a GP is a*r^(n - 1)

We have the common ratio as -4 and the 4th term is 16.

a*(-4)^3 = 16

=> a = -1/4

The first five terms are -1/4 , 1 , -4, 16 , -64

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let a1, a2, a3, a4, a5 are terms of G.P such that r= -4 is the common difference and a4 = 16

Then we know that:

a4 = a1*r^3

==> 16 = a1* -4*3

==> 16 = a1*-64

==> a1= -16/64 = -1/4

==> a2= a1* r= -1/4 * -4= 1

==> a3= a1*r^2= -1/4* 16 = -4

==> a4= a1*r^3 = -1/4* -64 = 16

==> a5= a1* r^4 = -1/4* 256 = -64

==> Then the first 5 terms are:

-1/4....1.....-4......16......-64

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