Question

The sum of 5th and 9th term of an ap is 72 and sum of 7th and 12th term of an ap is 97.find ap

Answer 1

Answer:

here is your answer

Step-by-step explanation:

let the first term of Ap be a and the difference be d

the question says

5th term + 9 th term =72

a+4d+a+8d=72

2a+12d=72

divide by 2

a+6d=36-------(1)

and

7th term + 12th term= 97

a+6d+a+11d=97

from (1)

36+a+11d=97

a+11d=61------(2)

by solving (1) and (2)

we get

a=6 and d=5

So AP is 6,11,16,21,26.......

Answer 2

Answer:

ARITHMETIC PROGRESSION PROBLEM SOLVING!

TO FIND : THE A.P

Let "a" be the first term and "d" be the common difference.

Given that in the Question ;-

a₅ + a₉ = 72 and, a₇ + a₁₂ = 97

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

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

Then we have,

2a + 12d = 72  -- ( 1 )

2a + 17d = 97 --- ( 2 )

Subtract ( 1 ) from ( 2 )

5d = 25

d = 5

Put the value of d in ( 1 ) we get :-

2a+60 = 72

2a = 12

a=6

Therefore, a = 6

and d= 5

Hence, the A.P will be 6,11,16,21

Step-by-step explanation:

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