Question

A sequence is defined by a recursive formula a1: -6 an: an-1 +2n write out the next three terms of this sequence

Answer 1

Answer:

• $a_{1} =-6$
• ${\displaystyle a_{2}=-2}$
• ${\displaystyle a_{3}=4}$
• ${\displaystyle a_{4}=12}$

Step-by-step explanation:

As the given recursive formula

${\displaystyle a_{n}=a_{n-1}+2n}$

and

$a_{1} =-6$

So, we have to determine the next three terms i.e. $a_{2}, a_{3},a_{4}$

Determining the value of $a_{2}$

As

${\displaystyle a_{n}=a_{n-1}+2n}$

Putting $n = 2$ to find $a_{2}$

${\displaystyle a_{2}=a_{2-1}+2(2)}$

${\displaystyle a_{2}=a_{1}+4}$

${\displaystyle a_{2}=(-6)+4}$         ∵a₁=-6

${\displaystyle a_{2}=-2}$

Determining the value of $a_{3}$

As

${\displaystyle a_{n}=a_{n-1}+2n}$

Putting $n = 3$ to find $a_{3}$

${\displaystyle a_{3}=a_{3-1}+2(3)}$

${\displaystyle a_{3}=a_{2}+6}$

${\displaystyle a_{3}=(-2)+6}$         ∵a₂=-2

${\displaystyle a_{3}=4}$

Determining the value of $a_{4}$

As

${\displaystyle a_{n}=a_{n-1}+2n}$

Putting $n = 4$ to find $a_{4}$

${\displaystyle a_{4}=a_{4-1}+2(4)}$

${\displaystyle a_{4}=a_{3}+8}$

${\displaystyle a_{4}=(4)+8}$         ∵a₃=4

${\displaystyle a_{4}=12}$

So,

• $a_{1} =-6$
• ${\displaystyle a_{2}=-2}$
• ${\displaystyle a_{3}=4}$
• ${\displaystyle a_{4}=12}$

Keywords: sequence, recursive formula, terms

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