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 β 4 = 5
- 14 β 9 = 5
- 19 β 14 = 5
Thus,
- a = 4
- d = 5
The formula to find the nth term of the Arithmetic Progression:
an= a + (n β 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)Γ5
β 105/5 = (n-1)
β 21 = (n-1)
β n = 21 + 1
β 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 β 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 β¦
a1 = a = 20
a2 = a1 + d = 20 + 2 = 22
a3 = a2 + d = 22 + 2 = 24
a4 = a3 + d = 24+ 2 = 26
And so onβ¦
Therefore, the A.P. is 20, 22, 24,26β¦
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 β 1)d.
here,
- n = 13
- a = 6
- d = 3
We need to find the 13th term.
Therefore:
an= 6 + ( 13- 1 )3
β an= 42
Hence, the 13th term is 42.