Question

The ninth term of an AP is equal to seven times the second term and twelfth term exceeds five times the third term by 2. Find the first term and the common difference.

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation:

Given :-

The ninth term of an AP is equal to seven times the second term.

Twelfth term exceeds five times the third term by 2.

To Find :-

a = ?? and d = ??

Solution :-

Let the first term of A.P. be a and common difference be d.

Given, a(9) = 7a(2)

or, a + 8d = 7(a + d)  .... (i)

And, a(12) = 5a(3) + 2

Again, a + 8d = 5(a + 2d) + 2 ...(ii)

From (i), a + 8d = 7a + 7d

⇒ - 6a + d = 0 .... (iii)

From (ii), a + 11d = 5a + 10d + 2

⇒ - 4a + d = 2 .... (iv)

Subtracting (iv) from (iii), we get

⇒ - 2a = - 2

⇒ a = 2/2

⇒ a = 1

From (iii),

⇒ - 6 + d = 0

⇒ d = 6

Hence, the first term is 1 and the common difference is 6.