Question

How many terms are there in arithmetic progression 15,21,27....279?

Answer 1

Step-by-step explanation:

it is a very easy question and remember the formula

Answer 2

There are 45 terms in the arithmetic progression 15 , 21 , 27 , . . . . , 279

Given :

The arithmetic progression 15 , 21 , 27 , . . . . , 279

To find :

The number of terms in the arithmetic progression

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

15 , 21 , 27 , . . . . , 279

Step 2 of 3 :

Write down first term and common difference

The arithmetic progression is

15 , 21 , 27 , . . . . , 279

First term = a = 15

Common Difference = d = 21 - 15 = 6

Step 3 of 3 :

Find the number of terms

Let number of terms in the AP = n

Then nth term of the AP = 279

a + ( n - 1 )d = 279

⇒ 15 + ( n - 1 ) × 6 = 279

⇒ 15 + 6n - 6 = 279

⇒ 6n + 9 = 279

⇒ 6n = 270

⇒ n = 45

There are 45 terms in the arithmetic progression 15 , 21 , 27 , . . . . , 279

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