Nth term of AP from First Two Terms

Given two integers a1 and a2, the first and second terms of an Arithmetic Series respectively, the problem is to find the n^th term of the series. 
Examples :

Input : a1 = 2, a2 = 3, n = 4
Output : 5
Explanation : The series is 2, 3, 4, 5, 6, .... , thus the 4th term is 5.

Input : a1 = 1, a2 = 3, n = 10
Output : 19
Explanation: The series is: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21..... Thus,10th term is 19.

[Naive Approach] - Using for Loop

In an Arithmetic Series, the difference between all pair of consecutive terms is same, for example, 2, 5, 8, 11, 14,,,,, The common difference is 3.

• Find the common difference of the series, common difference d = a2 - a1
• Run a loop to iterate over each term in the series from a1, keep adding common difference d until the n-th term is reached.

5

Time Complexity- O(n)
Auxiliary Space - O(1)

[Expected Approach] - Using the Formula for nth Term

To find the n^th term in the Arithmetic Progression series we use the simple formula . 

We know the Arithmetic Progression series is like = 2, 3, 4, 5, 6. …. … 
In this series 2 is the first term and 3 is the second term of the series . 
Common difference = a2 - a1 = 3 – 2 = 1 (Difference common in the series). 
so we can write the series as :
t₁ = a₁
t₂ = a₁ + (2-1) * d 
t₃ = a₁ + (3-1) * d 
. 
. 
. 
t_N = a₁ + (n-1) * d

t_N = a₁ + (n-1) * (a2-a1)

5

Time Complexity- O(1)
Auxiliary Space - O(1)