Question

find the number of terms in the following G.P.
1.) 4,8,16,...,8192.
2.) 1/3,1/9,1/27,...,1/2187.​

Answer 1

añ=a¹(r)^(n-1)

1. a¹=4; añ=8192; r=8/4=2

8192=4(2)^(n-1)

2^(n-1)=8192/2

2^(n-1)=4096

2^(n-1)=2^12

since base is same, equate the exponents

n-1=12

n=13

2. a¹=1/3; añ=1/2187; r=1/9÷1/3 =1/3

1/2187=1/3×(1/3)^n-1

1/729=(1/3)^n-1

(1/3)^6=(1/3)^n-1

n-1=6

n=7