Open In App

Which term of the progression 4, 9, 14, 19 is 109?

Improve
Improve
Like Article
Like
Save
Share
Report

Problem Statement: Which term of the progression 4,9, 14, 19 is 109

Solution:

Given:

  • a = 4
  • d = 5

The formula to find the nth term of the Arithmetic Progression:

an= a + (n – 1) d.

here, 

an= 109, a= 4, and d= 5 and we need to find the n.

Therefore: 

109 = 4+(n-1)×5

105/5 = (n-1)

n = 22

Hence, 109 is the 22nd term of the Arithmetic Progression.

Formula for n term of AP

Formula for the nth term of the Arithmetic Progression is given by:

an= a + (n – 1)d

where:

  • a = first term
  • d = common difference

Similar Questions

Question 1: Write the A.P. when the first term is 20 and the common difference is 2.

Solution:

Given:

  • a = 20
  • d = 2

Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 â€¦

a1 = a = 20

a= a1 + d = 20 + 2 = 22

a3 = a2 + d = 22 + 2 = 24

a4 = a+ d = 24+ 2 = 26

And so on…

Therefore, the A.P. is 20, 22, 24,26…

Question 2:  Find the 13th term of an AP if the first term is 6 and the common difference is 3.

Solution:

Given:

  • a = 6
  • d = 3

Formula to find the nth term of the Arithmetic Progression:

an= a + (n – 1)d.

here,

  • n = 13
  • a = 6
  • d = 3

We need to find the 13th term.

Therefore:

an= 6 + ( 13- 1 )3

an= 42

Hence, the 13th term is 42.


Last Updated : 18 Mar, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads