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What is the 14th term of the given sequence
64,-32,16,-8….

1 Answer

3 votes

Answer:


-(1)/(128)

Explanation:

1) Identify the type of sequence this is; whether it is geometric progression, quadratic sequence or linear sequence.

= Geometric progression

2) Find the
n^(th) term of this sequence. Every sequence of geometric progression is written in
u_(n) = u_(1) * r^(n-1) form, where
u_(1) is the first term of the sequence and
r is the common ratio. To find the
n^(th) term of this sequence, we need to find the common ratio (
r) first.


r = (u_(2))/(u_(1))


r = (-32)/(64)


r = -(1)/(2)

2.1) Write it in
u_(n) = u_(1) * r^(n-1) form.


u_(n) = 64 * (-(1)/(2) )^(n-1)

3) Find the
14^(th) term by substituting 14 into the
n's.


u_(14) = 64 * (-(1)/(2) )^(14-1)


u_(14) = 64 * (-(1)/(2) )^(13)


u_(14) = 64 * -(1)/(8192)\\u_(14) = -(1)/(128)

User Arthursfreire
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