Question

Is the sequence geometric? If it is, what are a₁ and r ?

c. 2³, 2⁷, 2¹¹, 2¹⁵, . . . . . . . .

Answer 1

a₁ = 8 and r = 16

Explanation:

the sequence has a common ratio r between consecutive terms and is therefore geometric , that is

r =
`(a_(2) )/(a_(1) )` =
`(2^(7) )/(2^3)` =
`2^((7-3))` =
`2^(4)` = 16

r =
`(a_(3) )/(a_(2) )` =
`(2^(11) )/(2^7)` =
`2^((11-7))` =
`2^(4)` = 16

r =
`(a_(4) )/(a_(3) )` =
`(2^(15) )/(2^(11) )` =
`2^((15-11))` =
`2^(4)` = 16

the first term a₁ = 2³ = 8