Question

(9.) In a geometric sequence, it is known that a1= -1 and a4= 64. The value of a10 is...

Answer 1

`a_(10) =262,144`.

Explanation:

Given :

In a geometric sequence ,
`a_(1) = -1\\a_(4) =64`

To Find : Value of
`a_(10)`

Solution :

Formula of finding nth term in geometric sequence :

`a_(n) =a_(1) *r^(n-1)`

Now to find values of r (common ratio)

`a_(4) =a_(1) *r^(4-1)`

`64 = -1*r^(3)`

`\sqrt[3]{-64} =r`

`-4 = r`

Now Find the value of
`a_(10)` using formula given above :

`a_(10) =a_(1) *r^(10-1)`

`a_(10) = -1 *(-4)^(9)`

`a_(10) = -1 *-262,144`

`a_(10) =262,144`

Hence The value of
`a_(10) =262,144`.

Answer 2

To fin the
`a_(10)`, we need to find the value of r first. And we are going to do that using the formula
`a_(n) = a_(1) .r^(n-1)`


`a_(4) = a_(1) . r^(4-1)`
We know that
`a_(1) =-1` and
`a_(4) =64`, so we can replace that in our equation to get:


`64=-1. r^(3)`
Now we can solve for r:

`r ^(3) = (64)/(-1)`

`r^(3) =-64`

`r= \sqrt[3]{-64}`

`r=-4`

Finally, we can use r to fin
`a_(10)` like this:

`a_(n) = a_(1) . r^(n-1)`

`a_(10) =(-1) (-4^(10-1) )`

`a_(10) =(-1)( -4^(9) )`

`a_(10) = (-1)(-262144)`

`a_(10) = 262144`

We can conclude that the answer is (2) 262,144