In an arithmetic sequence, the nth term an is given by the formula an=a1+(n−1)d, where a1 is the first term and d is the common difference. Similarly, in a geometric sequence, the nth term is given by 1an=a1•rn−1, where r is the common ratio. Use these formulas to determine the indicated term in the given sequence.

The 10th term of 40,10, 5/2, 5/8, ....

Question

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erinna erinna · Answer 1 · 2019-09-17T09:20:56+02:00

Answer:

The 10th term of given sequence is [tex]\frac{5}{32768}[/tex].

Step-by-step explanation:

The given sequence is

[tex]40,10, \frac{5}{2}, \frac{5}{8}, ....[/tex]

The given sequence is a geometric sequence because it have common ratio.

[tex]r=\frac{10}{40}=\frac{\frac{5}{2}}{10}=\frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}[/tex]

In the given sequence the first term of the sequence is 40.

[tex]a_1=40[/tex]

The nth term of a GP is

[tex]a_n=a_1r^{n-1}[/tex]

where, [tex]a_1[/tex] is first term and r is common ratio.

Substitute [tex]a_1=40[/tex] and [tex]r=\frac{1}{4}[/tex] in the above formula.

[tex]a_n=40(\frac{1}{4})^{n-1}[/tex]

Substitute n=10 , to find the 10th term.

[tex]a_{10}=40(\frac{1}{4})^{10-1}[/tex]

[tex]a_{10}=\frac{5}{32768}[/tex]

Therefore the 10th term of given sequence is [tex]\frac{5}{32768}[/tex].