Consider the sequences a. {a_n} = { -2, 5, 12, 19,...} b.

Caleb Snyder

Caleb Snyder

Answered question

2022-01-23

Consider the sequences
a. {an}={2,5,12,19,}
b. {bn}={3,6,12,24,48,}
(a) Find the next two terms of the sequence.
(b) Find a recurrence relation that generates the sequence.
(c) Find an explicit formula for the nth term of the sequence.

Answer & Explanation

sphwngzt

sphwngzt

Beginner2022-01-24Added 11 answers

1)Given sequence is an arythmetic sequence
First term a1=2
Common difference d=5(2)=5+2=7
Next two terms are
a5=a1+(51)d=2+(4)7=2+28
a5=26
a6=a1+(61)d=2+(5)7=2+35
a5=33
Recurrence formula:
a1=2
an=an1+7
Explicit formula
a5=a1+(n1)d
2)Given sequence is a multiple of 2
First term a1=3
Next two terms:
a6=2a5=2(48)=96
a7=2a6=2(96)=192
Recurrence formula
a1=3
an=2an1
Explicit formula
an=3(2)n1

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