Question

Which term of an AP 4,9,14,19,......... is 109

Answer 1

Answer:

a = 4

d = 5

Tn = 109

Tn = a + (n-1)d

109 = 4 + (n-1)5

105 = 5n -5

5n = 110

n. = 22

Hence, 22nd term of the AP is 109.

ANKIT KUMAR

Answer 2

22nd term of the AP 4 , 9 , 14 , 19 . . . . is 109

Given :

The arithmetic progression 4 , 9 , 14 , 19 . . . .

To find :

Which term of the AP 4 , 9 , 14 , 19 . . . . is 109

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

4 , 9 , 14 , 19 . . . .

Step 2 of 3 :

Write down first term and common difference

The arithmetic progression is

4 , 9 , 14 , 19 . . . .

First term = a = 4

Common Difference = d = 9 - 4 = 5

Step 3 of 3 :

Find which term of the AP 4 , 9 , 14 , 19 . . . . is 109

Let nth term of the AP 4 , 9 , 14 , 19 . . . . is 109

Then nth term of the AP = 109

a + ( n - 1 )d = 109

⇒ 4 + ( n - 1 ) × 5 = 109

⇒ 4 + 5n - 5 = 109

⇒ 5n - 1 = 109

⇒ 5n = 110

⇒ n = 22

Hence 22nd term of the AP 4 , 9 , 14 , 19 . . . . is 109

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