Question

If the sequence is 5,8,12.8, 20.48, is the sequence arithmetic or geometric? What is the general term? What is the seventh term?

Answer 1

Answer:

the common ratio is 5/8 for the given sequence.

Would you like to suggest the next number?

Step-by-step explanation:

Answer 2

Answer:

a) The sequence is geometric

b) $t_n=5\times \left (\frac{8}{5} \right )^{n-1}$

c)  Seventh term = 83.88608

Step-by-step explanation:

If it is an arithmetic progression common difference will be same,

       8 - 5 = 3

        12.8 - 8 = 4.8

Since common difference is not same the numbers are not arithmetic.

If it is an geometric progression common ration will be same,

                $\frac{8}{5}\\\\\frac{12.8}{8}=\frac{8}{5}\\\\\frac{20.48}{12.8}=\frac{8}{5}$

Since common ratio is same the numbers are geometric.

b) General term of GP is given by

                    $t_n=ar^{n-1}=5\times \left (\frac{8}{5} \right )^{n-1}\\\\t_n=5\times \left (\frac{8}{5} \right )^{n-1}$

c) Seventh term means n = 7

               $t_7=5\times \left (\frac{8}{5} \right )^{7-1}=5\times \left (\frac{8}{5} \right )^{6}=83.88608$

          Seventh term = 83.88608