Question

10) Given a,4,8,... is a geometric sequence. Find the value of a and the 10th term and 20th term.​

Answer 1

We need to find the formula of the sequence.

The general formula of a geometric sequence is
`a_n=ar^(n-1)`.

We know that
`r=(a_n)/(a_(n-1))`, so
`a=(a_2)/(r)`.

Therefore
`r=(8)/(4)=2` and
`a=(4)/(2)=2`.

So
`a_n=2\cdot 2^(n-1)=2^n`.

Therefore

`a_(10)=2^(10)=1024\\a_(20)=2^(20)=1048576`