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To find any term of a geometric sequence from another one you need the common ration between terms:

t{n} = t{n-1} × r = t{1} × r^(n-1)

where t{1} is the first term

and n is the required term.

It depends what was given in the geometric sequence ABOVE which you have not provided us.

I suspect that along with the 10th term, some other term (t{k}) was given; in this case the common difference can be found:

t{10} = 1536 = t{1} × r^9

t{k} = t{1} × r^(k-2)

→ t{10} ÷ t{k} = (t{1} × r^9) ÷ (t{1} × r^(k-1))

→ t{10} ÷ t{k} = r^(10-k)

→ r = (t{10} ÷ t{k})^(1/(10-k))

Plugging in the values of t{10} (=1536), t{k} and {k} (the other given term (t{k}) and its term number (k) will give you the common ratio, from which you can then calculate the 11th term:

t{11} = t(1) × r^9 = t{10} × r

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9y ago

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