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klemol [59]
3 years ago
14

If the 11th term of a geometric sequence is 32 times larger than the 6th term, then

Mathematics
1 answer:
mojhsa [17]3 years ago
4 0

Answer:

r = 2

Step-by-step explanation:

nth term of a geometric sequence = ar^{n - 1}.

Where,

a = first term, r = common ratio,

We are given that, the 11th term is 32 times larger than the 6th term of the geometric sequence. Thus:

the 6th term can be expressed as ar^{n - 1} = ar^{6 - 1}

a_6 = ar^{5}

The 11th term is expressed as a_11 = ar^{10}

Since the 11th term is 32 times larger than the 6th term, therefore, the following equation can be derived to find the common ratio, r, of the sequence:

a_11 = 32*a_6

a_11 = ar^{10}

a_6 = ar^{5}, therefore:

ar^{10} = 32*ar^{5}

Divide both sides by ar⁵

\frac{ar^{10}}{ar^5} = \frac{32*ar^{5}}{ar^5}

r^5 = 32

r^5 = 2^5

r = 2

Common ratio = 2

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