Question

if the term of an Arithmetic progression exceeds its 10th term by 7. Find the common difference

Answer 1

As we know the formula to finding the nth term i.e.
An = a +( n-1) d
So, A10 = a + 9d
And, A17 = a + 16d

Now, As per the question,
A17 - A10 = 7
a + 16d - (a+9d) = 7
7d = 7
d = 1.
So, the common difference is 1.

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Answer 2

We know that an = a+(n-1)*d

17th term of an A.P t17 = a + (17-1)* d = a+16d.

10th term of an A.P t10 = a + (10-1) * d = a+9d.

Given, 17th term of an AP Exceeds its 10th term by 7.

(a+16d) - (a+9d) = 7

a+16d - a - 9d = 7

16d - 9d = 7

7d = 7

d = 1.

The common difference is 1.