Question

if the 17th term of an a.p excedsits 10th term by 14 then find the common difference​

Answer 1

Answer:

The common difference of this A.P. is 2.

Step-by-step explanation:

What is an A.P. ?

An arithmetic progession is a list of numbers in which, each term is obtained by adding a fixed number to the preceding term except the first term.

Now coming to our question

First you should know how to find the arithmetic progression.

$a_n=a+(n-1)d$

$Where,\ a_n\ is\ the\ general\ term\ of\ the\ A.P.$

a is the first term of the A.P.

d is the common difference of the A.P.

n is the term of the A.P.

So, the 17th term of the A.P. will be given by

$17_{th}=a+(17-1)d\\17_{th}=a+(16)d\\17_{th}=a+16d$

Now, the 10th term can be given by the equation

$10_{th}=a+(10-1)d\\10_{th}=a+(9)d\\10_{th}=a+9d$

Now, it given, that the 17th term exceeds the 10th term by 14.

So, the equation will become

$a+16d=a+9d+14\\16d-9d=14\\7d=14\\ \therefore\; d=2$