How many terms of the series 51, 47, 43, 39 .............. be taken to make the sum of 330?

a) 7

b) 12

c) 10

d) 15

Given , AP = 51 ,47,43, 39 AND Sn=330

TO FIND - n=?

We know that

             S_n =n/2(2a + (n-1)d )

       Putting  a=51, d=(47-51 )= -4 and Sn =330

   330= n/2 (2*51 +(n-1)(-4) )

    330 = n/2*2 (51+(n-1)(-2))

330 = n(51-2n +2 )

330=n(53 -2n)

-2n² +53n-330=0

2n² -53n+330 =0

2n² -20n -33n +330 =0

2n(n-10 )-33(n-10 )=0

(n-10 )(2n-33)=0

Clearly n=10 as n cannot be 33/2

Therefore  c)10 is right answer

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