Question

Find the next three terms in the geometric sequence. Write any terms as fractions, if necessary. 1024, -128, 16,

Answer 1

The next three terms of the geometric sequence is 8192, 65,536,

Step-by-step explanation

Find the next three terms in the geometric sequence.

16, 128, 1024

`\begin{gathered} \text{The nth term of a geometric sequence} \\ T_n=ar^(n-1) \\ \text{where a = first term} \\ n\text{ = number of term} \\ a\text{ = 16} \\ r\text{ = common ratio} \\ \text{common ratio =}(128)/(16)\text{ = 8} \\ (1024)/(128)\text{ = 8} \\ T_1=16,T_2=128,T_3\text{ = 1024} \\ T_4=ar^(4-1) \\ T_4=16\cdot8^3 \\ T_4=\text{ 16 x 512} \\ T_4=\text{ 8,192} \\ T_5=ar^{5\text{ - 1}} \\ T_5=\text{ 16 }\cdot8^4 \\ T_5=16\text{ x 4096} \\ T_5=\text{ 65, 536} \\ T_6=ar^{6\text{ -1}} \\ T_6=\text{ 16 }\cdot8^5 \\ T_6=\text{ 16 x 32768} \\ T_6=\text{ 524, 288} \\ \text{The next thre}e\text{ terms are 8192, 65536, 524,288} \end{gathered}`