Question

if the starting term of an AP is 19 and the 6th& 22nd terms are in the ratio 11:31. Find the common difference.
Please help me​

Answer 1

Answer:

The first term A1 = 10 and common difference d = 2.

Step-by-step explanation:

Given,

6th term A6 = 20

11th term A11 = 30

We have, An = A1 + (n - 1) d

=> A6 = A1 + (6 - 1) d

=> 20 = A1 + 5d (equation 1)

A11 = A1 + (11 - 1) d

=> 30 = A1 + (11 - 1) d

=> 30 = A1 + 10d (equation 2)

Equation 1 & 2, we have

=> d = 2, substituting in (equation 1)

=> 20 = A1 + 5 (equation 2)

=> A1 = 20 - 10 = 10

Hence, the first term A1 = 10 and common difference d = 2.