Question

Find the common difference of the A.P., if a = 100 and t20 = 176.​

Answer 1

$\huge \pink{\mathfrak{solution}}$

Given:

◆ First term (a)= 100

and

◆ 20th term (t20)= 176

To find : Common difference(D)

● t20= 176

=>a+19d= 176

=>100+19d=176

=> 19d= 176-100

=> 19d= 76

=>d = 76/19

=> d = 4

Hence, the common difference is

$\boxed{ \red{\bold{4} }}$

Answer 2

SOLUTION:-

Given:

In Arithmetic progression a= 100 and 20th term=176.

To find:

The common difference of an A.P.

Explanation:

We have,

• First term of an A.P. is a=100.
• 20th term=176

According to the question:

We know that formula of the A.P.

nth term= an=a+(n-1)d

So,

20th term= 100+(20-1)d=176

⇒ 100+(19)d=176

⇒ 100+19d=176

⇒ 19d=176-100

⇒ 19d= 76

⇒ d= $\frac{76}{19}$

⇒ d= 4

Thus,

The common difference of an A.P. is 4.

Remark

• The nth term of A.P. is called general term.