Question

the sum of 5th and 9th terms of an AP is 72 and the sum of 7th and 12th term is 97.

Answer 1

a5 +a9=72
a+4d+a+8d=72
2a+12d=72............eq1

and
a7+a12=97
a+6d+a+11d=97
2a+17d=97.............eq2
subtracting eq1 from eq2
2a+17d=97
2a+12d=72
(-) (-) (-)
__________
5d=25
d=25/5
d=5
put d=5 in eq1
2a+12(5)=72
2a+60 =72
2a=72-60
a=12/2
a=6

I hope it helps now u can also find any term bcoz u now know the value of n and a....

Answer 2

The value of a is 6 and the A.P is 6, 11, 16,...

Given,

The sum of the 5th and 9th term of an AP is 72 and the sum of the 7th and 12th term is 97.

To Find,

The value of a and the A.P.

Solution,

The formula of nth term of an A.P is

a = a+(n-1)d

where,

a = First value of the AP

n = number of terms in AP

d = difference between two terms in the AP

So, according to the question

a + 4d + a + 8d = 72

2a + 12d = 72   ---------(1)

a + 6d + a + 11d = 97  

2a + 17d = 97   ---------(2)

(2) - (1), we get,

2a + 17d - 2a - 12d = 97 - 72

5d = 25

d = 25/5

d = 5   ----------(3)

Putting (3) in (1), we get,

2a + 12(5) = 72

2a + 60 = 72

2a = 72 - 60

2a = 12

a = 12/2

a = 6

Now, the A.P will be

a = 6

a₂ = 6+5 = 11

a₃ = 6+10 = 16

Hence, the value of a is 6 and the A.P is 6, 11, 16,...

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