Question

State the fifth and seventh terms of the sequence -2, -3, -4½..​

Answer 1

see explanation

Explanation:

there isa common difference between consecutive terms, that is

`(a_(2) )/(a_(1) )` =
`(-3)/(-2)` =
`(3)/(2)`

`(a_(3) )/(a_(2) )` =
`(-4(1)/(2) )/(-3)` =
`(3)/(2)`

this indicates the sequence is geometric with nth term

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = - 2 and r =
`(3)/(2)` , then

`a_(n)` = - 2
`((3)/(2)) ^(n-1)` , thus

a₅ = - 2 (
`((3)/(2)) ^(4)` = - 2 ×
`(81)/(16)` = -
`(81)/(8)`

and

a₇ = - 2
`((3)/(2)) ^(6)` = - 2 ×
`(72 9)/(64)` = -
`(729)/(32)`