Find the 20th term of an AP whose 3rd term is 7 and the 7th term exceeds three times the 3rd term by 2 . Also find its nth term ?




An arithmetic progression(AP) is a sequence of numbers such that the difference between any two consecutive terms is constant. The constant difference is called the common difference and is denoted by 'd'. In this problem, we have to find the 20th term of an AP whose 3rd term is 7 and the 7th term exceeds three times the 3rd term by 2. We also need to find its nth term.


- 3rd term of the AP = 7

- 7th term of the AP = 3 x 3rd term of the AP + 2


To find the common difference(d), we can use the formula:



d = a_n - a_n-1

where, a_n = nth term of the AP and a_n-1 = (n-1)th term of the AP


Using this formula, we can find the common difference(d) by considering the 3rd and 4th terms of the AP.

d = a₄ - a₃



Let's find a₄ using the formula:

a_n = a₁ + (n-1)d

where, a_n = nth term of the AP, a₁ = first term of the AP and d = common difference

Substituting the values, we get:

a₄ = a₁ + (4-1)d

a₄ = a₁ + 3d


We can also find a₃ using the same formula:

a₃ = a₁ + (3-1)d

a₃ = a₁ + 2d


Substituting these values in the formula to find d, we get:

d = (a₄ - a₃)/2

d = [(a₁ + 3d) - (a₁ + 2d)]/2



Simplifying, we get:

d = a₄ - a₃

d = 7 - a₃

d = 7 - (a₁ +