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A sequence is defined by the equations
a1=6 and an=2a n−1

. What is the fifth term in the sequence?

Sagot :

altavistard

Answer:

a(5) = 96

Step-by-step explanation:

Please use this notation:  a(1) = 6 and a(n) = 2a(n - 1).

In other words, each new term is twice the previous term.

Therefore, a(2) = 2a(1) = 2(6) = 12, and

                  a(3) = 2(12) = 24, and

                   a(4) = 48, and, finally,

                    a(5) = 96

Fifth term of the given sequence is equals to 96.

What is sequence?

" A sequence is defined as the arrangement of the given numbers or the object in such a way it represents some pattern or a mathematical rule."

According to the question,

Given,

First term of the sequence  a1 = 6

Nth term of the sequence   an  = 2a(n - 1)

Substitute the different values of 'n'  in the given sequence we get,

n = 2

a2 = 2a(2-1)

    = 2a1

    = 2 × 6

     = 12

n= 3

a3 = 2a(3-1)

    = 2a2

    = 2 ×1 2

    = 24

n= 4

a4 = 2a(4 - 1)

    = 2a3

    = 2 × 24

    = 48

Fifth term of the given sequence

n = 5

a5 = 2a(5 - 1)

    = 2a4

   = 2 × 48

  = 96

Hence, fifth term of the given sequence is equals to 96.

Learn more about sequence here

https://brainly.com/question/21961097

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