Question

check whether_150 is a term of the AP : 11,8,5,2....​

Answer 1

I hope the above picture perfectly helps you mate

Answer 2

No - 150 is not a term of the AP : 11 , 8 , 5 , 2 . . . .

Given :

The arithmetic progression 11 , 8 , 5 , 2 . . . .

To find :

To check - 150 is a term of the AP or not

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 3 :

Write down the given progression

Here the given arithmetic progression is

11 , 8 , 5 , 2 . . . .

Step 2 of 3 :

Write down first term and common difference

First term = a = 11

Common Difference = d = 8 - 11 = - 3

Step 3 of 3 :

Check - 150 is a term of the AP or not

If possible let - 150 is nth term of the AP

Then nth term of the AP = - 150

a + ( n - 1 )d = - 150

⇒ 11 + ( n - 1 ) × ( - 3 ) = - 150

⇒ 11 - 3n + 3 = - 150

⇒ - 3n + 14 = - 150

⇒ - 3n = - 164

⇒ n = 164/3

Now 164/3 is not a natural number

Hence - 150 can not be a term of the AP : 11 , 8 , 5 , 2 . . . .

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