Question

Sequencce (Xn) please?

Answer 1

See process below

Explanation:

Take a look to the first four terms

`6.5, -27.3, 114.66, -481.572,....`

First: we note that terms are alternate positive and negative, so the ratio is a negative number. Lets see

`-27.3/6.5=-21/5`
`114.66/-27.3=-21/5` and so on...

Then the comon ratio is `r=-21/5`

a) The recurrence system is `a_n=a_(n-1)·(-21/5)`

By other hand, we know that a geometric sequence has the general term given by

`a_n=a_1·r^(n-1)` where `a_0` is the first term `a_1=6.5=13/2`

Then `a_n=13/2·(-21/5)^(n-1)` This is the answer for b)

c) `a_8=13/2·(-21/5)^7=6.5xx-23053.93332=-149850.5666`

d) However the common ratio is bigger than 1, when n increase his value, the terms grow indefinitely alternating sign (the even terms are negatives and odd positives)