Question

the sum of 4th and 8th term of an ap is 22 and the sum of 6th and 8th term is 34 then find ap ​

Answer 1

$\textbf{\underline{\underline {Solution :}}}$

Sum of 4th and 8th term =22,

A6= a+3d+a8=a+7d=22

2a+11d=22....Equation (1)

Sum of 6th and 8th term =34

A6=a+5d+A8=a+7d=34

2a+13d=34...Equation (2)

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Now substitute Equation (1) from (2)

• 2a+13d=34
• 2a+11d=22

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No We have 2d=12

d=12/2

d=6

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Now put the value of d in equation (2) or (1) in which would you like to answer remains same

2a+13×6=34

2a+76=34

2a=76-34

2a=12

a=6

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Now put" 6" in the place of "a" so we got

• 2×6=12
• 3×6=18
• 4×6 =24

Hence the A.p of the given Question is 6,12,18,24,30.....!

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Answer 2

Hello !

Given:-

• $a_{4}$ + $a_{8}$ = 22
• $a_{6}$ + $a_{8}$ = 34.

To find:-

• A.P

Solution:-

$\implies$ a+3d+a+7d = 22

$\implies$ 2a+10d = 22

$\implies$ a+5d = 11 ........... eq.1

$\implies$ a+5d+a+7d = 34

$\implies$ 2a+12d = 34

$\implies$ a+6d = 17 ........... eq.2

Subtracting eq.1 from eq.2

$\implies$ a+6d-(a+5d) = 17-11

$\implies$ a+6d-a-5d = 6

$\implies$ d = 6.

now putting the value of d in eq.1

$\implies$ a+5d=11

$\implies$ a+5(6) = 11

$\implies$ a + 30 = 11

$\implies$ a = -19.

Hence, the A.P is -19, -13, -7.........