Question

5,9,13,...extra. What is its next term? Is 2021 is a term of this sequence

Answer 1

Step-by-step explanation:

Given :-

5,9,13,...

To find :-

What is its next term?

Is 2021 is a term of this sequence ?

Solution :-

Given sequence is 5,9,13,...

First term (a) = 5

Common difference (d)

=> 9-5 = 4

=> 13-9 = 4

Since the common difference is same throughout the sequence

=> They are in the AP.

We know that

The general term of an AP = an = a+(n-1)d

Next term = Fourth term

=> a4 = a+(4-1)d

=> a4 = a+3d

=> a4 = 5+3(4)

=> a4 = 5+12

=> a4 = 17

Next term = 17

And

Given term = 2021

Let an = 2021

=> a+(n-1)d = 2021

=> 5+(n-1)(4) = 2021

=> 5+4n-4 = 2021

=> 4n+1 = 2021

=> 4n = 2021-1

=> 4n = 2020

=> n = 2020/4

=> n = 505

2021 is 505th term of the AP

Answer:-

i) The next term of the AP is 17

ii) 2021 is in the given AP and it is 505th term of the AP.

Used formulae:-

• The general term of an AP = an
• = a+(n-1)d
• a = First term
• d = Common difference
• n = number of terms

Answer 2

Answer:

Step-by-step explanation:19 18