Question

Given two terms from a geometric sequence, identify the first term and the common ratio: a_10=1 and a_12=1/25

Answer 1

`a_(11)=a_(10)r`

`a_(12)=a_(11)r=a_(10)r^2`

Since
`a_(10)=1`, we have
`a_(12)=r^2=\frac1{25}`, which means
`r=\pm\frac15`.
Now,


`a_2=a_1r`

`a_3=a_2r=a_1r^2`

`\cdots`

`a_(10)=a_9r=\cdots=a_1r^9`

Since
`a_(10)=1` and
`r=\pm\frac15`, we get


`a_1=r^(-9)=\pm5^9`