Write 6 terms the geaometric progression such that the common difference is -3 and the 3rd term is 18.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The common ratio of the GP is -3 and the 3rd term is 18. Let the first term be a.

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

a*(-3)^2 = 18

=> a*9 = 18

=> a = 2

Now that we know a and r, we can determine the first 6 terms of the GP.

The first six terms of the GP are 2 , -6 , 18 , -54, 162, -486

hala718's profile pic

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

Posted on

Let us review the rules for the geometric progression.

Let a1, a2, a3, a4, a5, a6 are the first 6 terms is a G.P.

Let r be the common difference.

Then, we know that>

a1= a1

a2= a1*r

a3= a1*r^2

a4= a1*r^3

a5= a1*r^4

a6= a1*r^5

Given that r= -3 and a3 = 18

==> a3= a1*r^2

==> 18 = a1*-3^2

==> 18 = a1*9

==> a1= 18/9 = 2

==> a2= a1*r = 2*-3 = -6

==> a3= 18

==> a4= a1*r^3= 2*-3^3 = 2*-27 = -54

==> a5= 2*-3^4 = 2*81 = 162

==> a6= 2*-3^5 = -486

Then the first six terms are;

2, -6, 18, -54, 162, -486.

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