Question

Write the explicit formula for each sequence and use it to find the 10'' term of the sequence.

Answer 1

Answer:

Explicit formula for the sequence is $a_n=(-1)^{n+1}2^{n-1}$

$a_{10}=-512$

Step-by-step explanation:

Given: Sequence is $1,-2,4,-8,16,...$

To find: explicit formula for the sequence and the $10^{th}$ term of the sequence

Solution:

A sequence is an ordered list of numbers which repetitions are allowed and order does matter.

$a_1=(-1)^{1+1}\left [ 2^{(1-1)} \right ]=1\\a_2=(-1)^{2+1}\left [ 2^{(2-1)} \right ]=-2\\a_3=(-1)^{3+1}\left [ 2^{(3-1)} \right ]=4\\a_4=(-1)^{4+1}\left [ 2^{(4-1)} \right ]=-8\\a_5=(-1)^{5+1}\left [ 2^{(5-1)} \right ]=16$

So, explicit formula for the sequence is $a_n=(-1)^{n+1}2^{n-1}$

To find the $10^{th}$ term of the sequence, put n = 10

$a_{10}=(-1)^{10+1}\left [ 2^{(10-1)} \right ]\\=(-1)^{11}2^9\\=-1(2^9)\\=-512$