"Ifa1=2andan=2an−1,find the first five terms of the sequence.a1=…,a2=…,a3=…,a4=…,a5=…" solved and explained

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Kason Chang

Answered question

2022-04-23

If $a_{1} = 2$ and $a_{n} = 2 a_{n - 1}$ ,find the first five terms of the sequence.
$a_{1} = \dots$ , $a_{2} = \dots$ , $a_{3} = \dots, a_{4} = \dots$ , $a_{5} = \dots$

Answer & Explanation

Kendrick Fritz

Beginner2022-04-24Added 12 answers

Step 1

a_{1} = 2, a_{n} = 2 a_{n - 1}

For

n = 2

a_{2} = 2 a_{2 - 1} = 2 a_{1}

= 2 (2) = 4

Step 2

a_{2} = 4

For

n = 3

a_{3} = 2 a_{3 - 1} = 2 a_{2}

= 2 (4) = 8

a_{3} = 8

a_{4} = 2 a_{4 - 1} = 2 a_{3}

= 2 (8) = 16

a_{5} = 2 a_{5 - 1} = 2 a_{4}

= 2 (16) = 32

a_{5} = 32

∴

The five terms of the sequence are:

a_{1} = 2, a_{2} = 4, a_{3} = 8, a_{4} = 16, a_{5} = 32

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