Question

For a given geometric sequence, the common ratio, r, is equal to -2, and the 7th term, a7, is equal to 11. Find the value of the 10thterm, a10. If applicable, write your answer as a fraction.a10=

Answer 1

In general, a geometric sequence can be expressed as shown below

`\begin{gathered} a_n=a_1(r)^(n-1) \\ a_n\rightarrow\text{ n-th term} \\ r\rightarrow\text{ common ratio} \end{gathered}`

Thus, in our case, given that r=-2 and the 7th term is equal to 11,

`\begin{gathered} a_7=11 \\ \Rightarrow11=a_1(-2)^(7-1) \\ \Rightarrow11=a_1(-2)^6 \\ \Rightarrow a_1=(11)/((-2)^6)=(11)/(64) \\ \Rightarrow a_1=(11)/(64) \end{gathered}`

Then,

`\Rightarrow a_n=(11)/(64)(-2)^(n-1)`

Set n=10,

`\begin{gathered} \Rightarrow a_(10)=(11)/(64)(-2)^(10-1)=(11)/(64)(-2)^9=(11)/(64)(-512)=-88 \\ \Rightarrow a_(10)=-88 \end{gathered}`

Hence, the 10th term of the sequence is equal to -88.