# Write the Expression An- Ak For the A.P. A, a + D, a + 2d, ... Hence, Find the Common Difference of the A.P. for Which 20th Term is 10 More than the 18th Term. - Mathematics

Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which

20th term is 10 more than the 18th term.

#### Solution

A.P: a, a + d, a + 2d

Here, we first need to write the expression for a_n - a_k

Now as we know

a_n = a + (n -1)d

So for the nth term

a_n = a + (n - 1)d

So for the nth term

Similarly for kth term

a_k = a + (k - 1)d

So,

a_n - a_k = (a + nd - d) - (a + kd - d)

= a + nd - d -a - kd +    d

= nd - kd

= (n - k)d

So, a_n - a_k = (n - k)d

In the given problem, the 20th term is 10 more than the 18th term. So, let us first find the 20th term and 18th term of the A.P.

Here

Let us take the first term as a and the common difference as d

Now, as we know,

a_n = a + (n -1)d

So for 20th term (n = 120)

a_20 = a + (20 - 1)d

= a + 19d

Also for 18th term (n = 18)

a_18 = a + (18 - 1)d

= a + 17d

Now, we are given,

a_20 = a_18 + 10

On substituting the values, we get,

a + 19d = a + 17d + 10

19d - 17d = 10

2d = 10

d = 10/2

d = 5

Therefore, the common difference for the A.P. is d = 5

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 21.3 | Page 25