Question

the sum of 4 and 8 term of an Ap is 24 and sum of the 6 and 10 term is 34 find the first term and commo
n difference of the Ap​

Answer 1

Answer:

First term of AP = -1/2

Common difference = 5/2

Step-by-step explanation:

given that,

the sum of 4 and 8 term of an Ap is 24

let the first term be a

and common dufference be d

so,

According to the question,

a + (4 - 1)d + a + (8 - 1)d = 24

2a + 3d + 7d = 24

2a + 10d = 24

2(a + 5d) = 24

a + 5d = 24/2

a + 5d = 12 ....(1)

also,

given that,

sum of the 6 and 10 term is 34

so,

here we have,

a + (6 - 1)d + a + (10 - 1)d = 34

a + 5d + a + 9d = 34

2a + 14d = 34

2(a + 7d) = 34

a + 7d = 34/2

a + 7d = 17. ....(2)

now,

we have,

a + 5d = 12. ...(1)

a + 7d = 17. ....(2)

(1) - (2)

a + 5d - (a + 7d) = 12 - 17

a + 5d - a - 7d = -5

-2d = -5

d = -5/-2

d = 5/2

now,

putting the value of d on (1)

a + 5d = 12

a + 5(5/2) = 12

a + 25/2 = 12

a = 12 - 25/2

a. -1/2

so,

First term of AP = -1/2

Common difference = 5/2

Answer 2

Answer:-

a = -1/2.

d = 5/2

Given:-

$a_4 + a_8 = 24$

$a_6 + a_10 = 34$

To find :-

It's first term and common difference.

Solution:-

Let the first term be a and common difference be d.

A/Q.

→$a_4 + a_8 = 24$

→$a + 3d + a + 7d = 24$

→$2a + 10 d = 24 -----eq. 1$

Now ,

→$a_6 + a_10 = 34$

→$a +5d + a + 9d= 34$

→$2a + 14d = 34-----eq.2$

Subtract equation. 1 and equation 2. we get,

→$2a + 10d = 24 \\ 2a + 14 d = 34$

→$2a - 2a +10d -14d = 24 -34$

→$-4d = -10$

→$d =\dfrac{10}{4}$

→$d = \dfrac{5}{2}$

Now,

we have d = 5/2

Put its value in equation 1.

2a + 10 d = 24

→ 2a + 10 × 5/2 = 24

→ 2a +25 = 24

→ 2a = 24 -25

→ 2a = -1

→ a = -1/2

hence, the common difference will be 5/2 .

the common difference will be 5/2 . And, first term will be = -1/2.