Question

a8+a4=24,a6+a10=34.find common difference and first term

Answer 1

a+7d+a+3d = 24

a+5d = 12. (1)

A6 = 12.

a+5d+a+9d = 34

a+9d = 34-12

a+9d = 22. (2)

(2)-(1)

4d = 10

d = 5/2

a = 12-5d

= 12-12.5

= -1/2

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Answer 2

Given :

a8 + a4 = 24

and

a6 + a10 = 34

To find:

common difference (d ) and first term (a)

Solution:

we know that

a8= a+7d and

a4= a+3d

from given equations

(a+7d)+(a+3d) = 24

2a+10d = 24 -----(1)

similarly,

a6= a+5d &

a10= a+ 9d

(a+5d)+ (a+9d) = 34

2a+ 14d=34 -----(2)

By using elimination method

2a+10d=24

2a+14d=34

- - -

(2a will be canceled)

we will get

-4d = -10

d = 10/4

d= 5/2

d= 2.5

put d = 2.5 in eq (1)

2a + 10 × 2.5 =24

2a + 25 = 24

2a + 25= 24

2a = 24-25

a = -1/2

a = -1/2

Hence, common difference = 5/2 or 2.5 and first term = -1/2 or -0.5

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