ttregoning2006
Answered

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

-4096
2048
4096
-2048

Sagot :

A geometric sequence has a common ratio.

The formula for the nth term is

[tex]\sf{a_n =ar^{n-1} }[/tex]

where,

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

Given -

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

To find -

  • the 12th term of the given geometric sequence

Solution -

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

[tex]\rightarrow\sf{a_{12} =2(-2)^{12-1} }[/tex]

[tex]\rightarrow\sf{a_{12 }=2(-2)^{11} }[/tex]

[tex]\rightarrow\sf{a_{12} =2×(-2048) }[/tex]

[tex]\rightarrow\bf{a_{12 }=-4096 }[/tex]

Hence, the 12th term is -4096.

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