Question

Consider the following sequence

152, -76, 38, -19
Write a rule for the nth term and then find
`a_7`

Answer 1

Solution given:

first term [a]=152

second term[b]=-76

common ratio[r]=
`(-76)/(152)`=-1/2

now

for nth term ,we have

nth term =a
`{r}^(n -1)`

now

7th term==152
`{-1/2}^(7 - 1)`

=152×1/64=19/8

Answer 2

a₇ = 2.375

Explanation:

There is a common ratio r between consecutive terms, that is

r =
`(-76)/(152)` =
`(38)/(-76)` =
`(-19)/(38)` = -
`(1)/(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 = 152 and r = -
`(1)/(2)` , then

`a_(n)` = 152
`(-(1)/(2)) ^(n-1)` , so

a₇ = 152
`(-(1)/(2)) ^(6)` = 152 ×
`(1)/(64)` = 2.375