Question

the 9th term of an ap is equal to the seven times the second term and 12th term exceeds 5 times the third term by to find the first term and common difference

Answer 1

Let a be first term and d be common difference

9 th term = a+ 8 d

second term = a + d

As given

a + 8d = 7 ( a + d)

a + 8 d = 7a + 7d

- 6a = -d

6a = d

Now

12 th term = a + 11 d

third term = a + 2d

As given

a + 11 d= 5( a + 2d) + 2

a + 11 d = 5a + 10 d + 2

- 4a + d = 2

put 6 a = d

- 4a + 6 a = 2

2a = 2

a= 1

As 6a = d

d = 6

So first term = 1

common difference= 6

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Answer 2

A9=7*a2
a12=5a3+2

That means,
a9=(a+d)7
a12=5(a+2d)+2

That means,
a+8d=7a+7d, d=6a
a+11d=5a+10d+2,
d=4a+2,
2a=2,
a=1//
d=6a=6//

So first term is 1 & common difference is 6.


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