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Step2247 [10]
1 year ago
10

Given the following geometric sequence, find the 12th term: {2, -4, 8, ...}.

Mathematics
1 answer:
jolli1 [7]1 year ago
5 0

A geometric sequence has a common ratio.

The formula for the nth term is

\sf{a_n =ar^{n-1} }

where,

  • an = nth term of the sequence,
  • a = first term of the sequence and
  • r = common ratio

<u>Given</u> -

  • A geometric sequence 2, -4, 8, ...

<u>To find</u> -

  • the 12th term of the given geometric sequence

<u>Solution</u> -

A.T.Q, a = 2 and r = -2

\rightarrow\sf{a_{12} =2(-2)^{12-1} }

\rightarrow\sf{a_{12 }=2(-2)^{11} }

\rightarrow\sf{a_{12} =2×(-2048) }

\rightarrow\bf{a_{12 }=-4096 }

<u>Hence, the 12th term is -4096</u>.

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