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
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:
an= a + (n – 1) d.
where,
- an = nth term of AP
- a = First term of AP
- n = no. of term
- d = Common difference
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)
⇒ 21 = (n-1)
⇒ n = 21 + 1
⇒ n = 22
Hence, 109 is the 22nd term of the Arithmetic Progression.