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Valentin [98]
2 years ago
7

Find the first term and the explicit formula a12=1/32 and r=1/2

Mathematics
1 answer:
Alexxx [7]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

Given a_{12} = \frac{1}{32} and r = \frac{1}{2}, then

a (\frac{1}{2}) ^{11} = \frac{1}{32}, that is

\frac{a}{2^{11} } = \frac{1}{32}

\frac{a}{2048} = \frac{1}{32} ( cross- multiply )

32a = 2048 ( divide both sides by 32 )

a = 64 ← first term

Thus the explicit formula is

a_{n} = 64 (\frac{1}{2}) ^{n-1}

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