Math, asked by BrainlyHelper, 11 months ago

The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

Answers

Answered by nikitasingh79
14

Answer:

The required AP is 3, 5 ,7, 9 ,....

Step-by-step explanation:

Given:  

a19 = 3(a6) and a9 = 19  

Let the first term of an A.P be 'a' & Common difference be 'd'.

By using the formula , nth term , an = a + (n -1)d

Case : 1

a19 = 3(a6)

a + (19 -1)d = 3 ( a + (6 - 1) d

a + 18d = 3(a + 5d)

a + 18d = 3a + 15d

a - 3a + 18d - 15d = 0

-2a + 3d = 0 ………..(1)

 

Case : 2

a9 = 19  

a + (9 - 1)d = 19

a + 8d = 19

a = 19 - 8d…………(2)

On putting the value of 'a' in eq 1.

-2a + 3d = 0

-2(19 - 8d) + 3d = 0

- 38 + 16d + 3d = 0

- 38 + 19d = 0

19d = 0 + 38

19d = 38

d = 38/19

d = 2  

On putting the value of 'd' in eq 2,

a = 19 - 8d

a = 19 - 8(2)

a = 19 - 16

a = 3

First term , a = 3  

Second term ,a2 = a + d = 3 +2 = 5

Third term , a3 = a2 + d = 5 + 2 = 7

Fourth term, a4 = a3 + d = 7 + 2 =9

Hence, the required AP is 3, 5 ,7, 9 ,....

HOPE THIS ANSWER WILL HELP YOU...

Answered by vishakaa
6

hey mate....

here is your answer

Attachments:
Similar questions