Question

in an
AP the 10th term is 46 sum of the 5th and the 7th term is 52 find the AP

Answer 1

10th term = 46

a + 9d = 46

a = 46 - 9d ----1equation

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Sum of 5th & 7th term = 52

=> a+4d + a + 6d = 52

=> 2a + 10d = 52

=> a + 5d = 26

Now, putting the value of a from 1equation

=> 46 - 9d + 5d = 26

=> -4d = 26-46

=> -4d = -20

=> d = 20/4

=> d = 5

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Putting the value of d in 1equation,

a = 46 - 9d

a = 46 - 9(5)

a =46-45

a = 1

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A.P. =

1,(1+5), (1+10), (1+15)

I hope this will help you

-by ABHAY

Answer 2

Solution:-

Given : Sum of the 5th and 7th term is 52.

∴ a + 4d + a + 6d = 52

2a + 10d = 52 ...............(1)

Also given : 10th term is 46

∴ a + 9d = 46

Multiplying it by 2, we get

2a + 18d = 92 ................(2)

 Now, subtracting equation (1) from equation (2), we get.

  2a + 18d = 92

  2a + 10d = 52

-      -          -

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         8d = 40 

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8d = 40

d = 40/8

d = 5

 Substituting the value of d in equation (1),we get.

2a + 10d = 52

2a + 10*5 + 52

2a = 52 - 50

2a = 2

a = 2/2

a = 1

Therefore, the required AP is 1, 6, 11, 16, 21, 26, 31....