SEQUENCE AND SERIES A13

Find the number of terms in the following geometric progression 5+10+20+40+ … + 1280

Solution

G₁=5, G_n=1280, r=2.

G_n = G₁r^n-1;

1280 = 5 x 2^n-1;

1280 = 5 x 2^n-1;       (Divide by 5 on both sides)

   5         5

256 = 2^n-1;

256 = 2ⁿ x 2^-1;

256 = 2ⁿ x ¹/2;

256  =  2ⁿ;  (Divide by ¹/2 on both sides)

  ¹/2      

512 =  2ⁿ;     (512 = 2x2x2x2x2x2x2x2x2)

2⁹ =  2ⁿ;

9 = n

There are 9 terms in a Geometrical Progression.