SEQUENCE AND SERIES A2

Find the number of terms in the following geometric progression 2+6+18+54+ ….. + 1458

Solution

G₁=2, G_n=1458, r=3.

G_n = G₁r^n-1;

1458 = 2 x 3^n-1;

1458 = 2 x 3^n-1;

 2          2

729 = 3^n-1;

729 = 3ⁿ x 3^-1;

729 = 3ⁿ x ¹/3; (dividing by 1/3 on both sides)

729  =  3ⁿ;

  ¹/3      

2187 =  3ⁿ;

2187 =  3ⁿ;     (2187 = 3x3x3x3x3x3x3)

3⁷ =  3ⁿ;

7 = n

Hence There are 7 terms in a Geometrical Progression.