The sum of first three terms of an AP is 45. If the product of the first and the third term exceeds the second term by 21, find the AP. Please do not reply to see solution to similar question. After following similar solution getting the common difference in decimals. Please reply at the earliest. 

Dear Student,

Please find below the solution to the asked query:

Given : The sum of first three terms of an AP is 45 .

We know common difference in A.P. is same .

Let , three terms of A.P. =  a - d , a , a + d 

So,

a - d + a + a + d = 45

3 a = 45

a = 15

And

( a - d ) ( a + d ) - a = 21

$\Rightarrow$a² - d² - a =  21  , Substitute a =  15 and get

$\Rightarrow$15² - d² - 15  = 21

$\Rightarrow$225 - d² - 15  = 21

$\Rightarrow$d² = 225 - 15 - 21

$\Rightarrow$d² = 189

$\Rightarrow$d = 13.7477$\approx$13.75

So,

Terms 15 - 13.75  = 1.25  and 15 + 13.75  = 28.75

Therefore,

Our A.P. = 1.25 ,  15 ,  28.75                                                                           ( Ans )

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