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

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

Solution:

Since the common difference across all the numbers is the same, we can conclude that this series is in an Athematic progression:

• 9 – 4 = 5
• 14 – 9 = 5
• 19 – 14 = 5

Thus,

• a = 4
• d = 5

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

a_n= a + (n – 1) d.

where,

• a_n = n^th term of AP
• a = First term of AP
• n = no. of term
• d = Common difference

Here, 

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

Therefore: 

109 = 4+(n-1)×5

⇒ 105/5 = (n-1)

⇒ 21 = (n-1)

⇒ n = 21 + 1

⇒ n = 22

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

Formula for n term of AP

Formula for the n^th term of the Arithmetic Progression is given by:

a_n= 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 …

a₁ = a = 20

a₂ = a₁ + d = 20 + 2 = 22

a₃ = a₂ + d = 22 + 2 = 24

a₄ = a₃ + d = 24+ 2 = 26

And so on…

Therefore, the A.P. is 20, 22, 24,26…

Question 2:  Find the 13^th 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:

a_n= a + (n – 1)d.

here,

• n = 13
• a = 6
• d = 3

We need to find the 13th term.

Therefore:

a_n= 6 + ( 13- 1 )3

⇒ a_n= 42

Hence, the 13^th term is 42.