Question

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

-4096
2048
4096
-2048

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.