Question

In the Geometric Progressions (G.P.), the sum of the first 6 terms is 28 times the sum of the first 3 terms. Find the common ratio.

Answer 1

Step-by-step explanation:

S(6) = 28 * S(3)

a(r^6 - 1)/(r-1) = 28 * a(r³-1)/(r-1)

(r^6 - 1) = 28 (r³ - 1)

r^6 - 1 = 28r³ - 28

r^6 - 28r³ + 27 = 0

r^6 - 27r³ - r³ + 27 = 0

r³(r³ - 27) - ( r³ - 27 ) = 0

(r³ - 27) (r³ - 1) = 0

r = 3 , 1

Common ratio r = 1,3