Is the sequence arithmetic if so identify the common difference 13, 20, 27, 34?

Solution:

If the sequence a₁, a₂, a₃, ………. aₙ are in A.P then a₂ - a₁ = a₃ - a₂ = …. = common difference

Here, 20 - 13 = 27 - 20 = 34 - 27 = 7 thus the given sequence forms an A.P.

And the common difference is 7

Example: Find the common difference, general term and 10th term of the Arithmetic progression 3, 8, 13, 18, …..

Solution: If the sequence a₁, a₂, a₃, ………. aₙ are in A.P then a₂ - a₁ = a₃ - a₂ = … = common difference.

Here, common difference = :a₂ - a₁ = 8 - 3 = 5

The general term of A.P is aₙ = a + (n - 1)d , here ‘a’ is the first term, d is the common difference and ‘n’ is the number of terms.

Now a = 3, d = 5 ∴ General term = aₙ = 3 + (n - 1)5 = 5n - 2

And to find the 10th term, put a = 3, d = 5 and n = 10

a₁ₒ = 3 + (10 - 1) 5 = 48

Is the sequence arithmetic if so identify the common difference 13, 20, 27, 34?

Summary:

The given sequence is 13 20 27 34 in Arithmetic progression with common difference 7