What is the first term of a geometric sequence

Question

Find the first term of the geometric sequence with a₆ = 256 and a₇= 1024

Answer 1

Since a₆ = 256 and a₇ = 1024, r = common ratio = a₇/a₆ = 4

 

a_n = a₁r^n-1   So, a₆ = 256 = a₁(4)⁵

 

                              256 = 1024a₁

 

                               a₁ = 256/1024 = 1/4

Answer 2

for the first sequence: 

a₆=256=4*64=4*2⁶ thus, the first term of this sequence is 4

for the second one, we will follow the same procedure and we will find:

a₆=1024=16*64=16*2⁶, it means that the first of this sequence is 16.

 

I hope it will help,

 

regards,

 

Hassan