Question

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

Answer 1

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

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

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

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

$\rightarrow\sf{a_{12} =2×(-2048) }$

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

Hence, the 12th term is -4096.