Question

the sum of the 7th and 8th term of an ap is 4 x + 7 and its 11th term is 2 x + 5 find the first term and the common difference for X equals to 1​

Answer 1

Answer:

First term = 19/7

and Common difference = 3/7

Step-by-step explanation:

Let First term be a and common difference be d

Given:

x = 1

and a₇+a₈ = 4x+7

∴ a + 6d + a + 7d = 4x + 7

= 2a + 13d = 4x + 7

{Now, x = 1}

∴ 2a + 13d = 4 + 7

= 2a + 13d = 11                   [eqn 1]

also, a₁₁ = 2x + 5

= a + 10d = 2x+5

{x = 1}

∴ a + 10d = 2 + 5

= a + 10d = 7                     [eqn. 2]

{Now, multiply eqn 2 with 2}

∴ 2a + 20d = 14                [eqn 3]

Now, subtract eqn 1 from eqn 3:

∴ (2a + 20d) - (2a + 13d) = 14 - 11

= 2a + 20d - 2a - 13d =3

= 7d = 3

= d = 3/7

∴Common difference = 3/7

Now, put d = 3/7 in eqn 2:

∴ a + 10(3/7) = 7

= a + 30/7 = 7

= a = 7 - 30/7

= a = (49 - 30)/7

= a = 19/9

So, First term = 19/7

and Common difference = 3/7

Hope, you got it :-))

Please, mark it as brainiest!!