Question

how many terms are there in A.P. 15,21,27,.....
279?

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Answer 1

Answer:

a=15

d=21-15

d=6

an=279

a+(n-1)d=279

15+(n-1)6=279

(n-1)6=264

n-1=264/6

n-1=44

n=45

there are 45 terms in ap

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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