Question

All the terms pf an



a.P. Are natural numbers.Sum of its first nine terms lies between 200 and 22p,second term is 12,then find the common difference.

Answer 1

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$\huge\underline\mathfrak{Answer :}$

$\huge\underline\mathfrak{Solution :}$

Let the series be  a ,  a+d,  a+2d , .....

sum of the first 9 terms:    [2 a + 8 d] *

9/2 = 9 a + 36 d

   so  200 <= 9 a + 36 d <= 220

2nd term :  a + d = 12      =>  9a = 9 (12 - d) = 108 - 9 d

 =>  200 <= 108 - 9d + 36 d <= 220

  =>    92 <=  25 d <= 112

  =>     3.6 <=  d  <=  4.4

   => d = 4      as d is a natural number and  a is also a natural number.

   =>  a = 12 - 4 = 8.

series:  8, 12, 16, 20, 24, ...         

sum of the first 9 numbers: 216 .

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