Question

the sum(sn) of first 5 terms and 9 terms of ap is 72 and the of the first 7th and 12th term is 97 find the ap
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Answer 1

Given :

• the sum(sn) of first 5 terms and 9 terms of ap is 72 and the of the first 7th and 12th term is 97

To find :

• AP

Solution :

We are given that,

a_5+ a_9 = 72

'.a + 4d +a + 8d = 72

2a + 12d = 72..(I)

and a_7 +a_12 = 97

2a + 17d = 97 ..(ii)

on equating (i) and (ii), we get

5d = 25

d = 5

put d = 5 in eq. (i)

2a + 12(5) = 72

2a + 60 = 72

2a = 72 - 60

2a = 12

a = 6

then,

a_1 6,a_2 11, a_3 = 16, a_4 = 21,. so on

AP is 6, 11, 16, 21,..

Answer 2

Answer:

GIVEN :

The sum(sn) of first 5 terms and 9 terms of ap is 72 and the of the first 7th and 12th term is 97

___________

TO FIND :

• The AP

___________

ANSWER :

T 5 + T 9 = 72

WE KNOW : ANY TERM IN AP =

$a + (n - 1)d$

• Where a is the first term of AP
• d is the common difference

=) a + 4d +a + 8d = 72

2a + 12 d = 72

Dividing by 2

=) a + 6d = 36

=) a = 36 - 6d........i

_______

T7 + T 12 = 97

=) a + 6d + a + 11 d = 97

=) 2a + 17 d = 97

=)72 - 12 d + 17 d = 97 * Substituting value of a

=) 5d = 25

=) d = 5

Now in eq. i

• a = 36 -30
• a = 6

____________

AP :

6,11,17,22.......

×××××××××××××××××

Hope it helps

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