Question

Which expression would give the thirteenth term Given the sequence 8, 16, 32, 64, ...,

813
8 · 213
8 · 212 ? 813 8 · 213 8 · 212

Answer 1

if you notice, 8, 16, 32, 64 <--- 8 * 2 is 16, 16 * 2 is 32 and so on.

so, you get the next term's value by simply multiplying the "current term" by 2. So is a geometric sequence then.

therefore, the "common ratio" or multiplier is 2, and the first term's value is 8.


`\bf n^(th)\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1\\ n=13 \end{cases} \\\\\\ a_(13)=8\cdot 2^(13-1)\implies a_(13)=8\cdot 2^(12)\implies a_(13)=8\cdot 4096 \\\\\\ a_(13)=32768`