Question

Find the sum of first 6 terms of a GP whose fourth term
is 108 and seventh term
is 2916​

Answer 1

ar^3 = 108 - ( i ) & ar^6 = 2916 - ( ii )

Dividing ii by i

ar^6 2916

------ = ---------

ar^3 108

r^3 = 27

r = 3

ar^3 = 108

27a = 108

a = 4

Sum of 6 terms = a ( r^6 - 1 )

----------------

r - 1

= 4 ( 3^6 - 1 )

----------------

3 - 1

= 4 × 728

-----------

2

= 1456