Question

the ninth term of an AP is equal to the seventh time the second term and the twelth term exceeds five times the the third term by 2 find the first term and the common difference.
​

Answer 1

Step-by-step explanation:

mark it as brainiest and follow me

Answer 2

$\large\bf{\underline\pink{Good \: Night↝}}$

Question :-

The ninth term of an AP is equal to the seventh time the second term and the twelth term exceeds five times the the third term by 2 find the first term and the common difference.

Answer :-

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.