G.PROGRESSION J1

 The 1st term of a geometric progression is 7 and the 5th term is 112. Find i)the common ratio. ii) 12^th term

 

Solution

 

G₁=7, G₅=112, n=5

 

i) G_n = G₁r^n-1;

 

G₅ = G₁r^5-1;

 

G₅ = G₁r⁴;

 

112 = 7 x r⁴;

 

112 = 7r⁴;

 7       7

 

16 = r⁴;  Finding the fourth root of 16,

 

r = 2

 

 

 

Hence the common ratio is 2.

 

ii)  12^th term

 

G_n = G₁r^n-1;

 

G₁₂ = G₁r^12-1;

 

G₁₂ = G₁r¹¹;

 

G₁₂ = 7 x 2¹¹;

 

G₁₂ = 7 x 2048;

 

G₁₂ = 14336

 

Hence the 12th term is 14336

 

TRY THIS………………………….. 

 

The 1st term of a geometric progression is 2 and the 6th term is 486. Find i) the common ratio. ii) 10^th term