# Let     if     is such that a+b+c=3 and is equal to : Option 1) 165 Option 2) 190 Option 3) 255 Option 4) 330

As we learnt in

Summation of series of natural numbers -

- wherein

Sum of first n natural numbers

Summation of series of natural numbers -

- wherein

Sum of  squares of first n natural numbers

f(x) = ax+ bx + c

a + b + c = 3

f(x+y) = f(x) + f(y)+xy

Then

f(1) = a + b + c =3

f(1) =3

put  y = 1

f(2)= f(1) + f(1)+1  1

=2f(1)+1

=2  3+1=7

put x=1, y = 2

f(3)= f(1)+f(2)+2 1

=3+7+2

=12

f(1)+f(2)+(f3)+ ------= 3+7+12+ ---

Now

An2+Bn+C

put  n =1

3 = A+B+C

At n =2

7 = 4A+2B+C

At n =3

12 = 9A+3B+C

4 = 3A+B

5 = 5A+B

1= 2A

B+C =

2B+C

=7-2 = 5

C=0

So

put n =10

= 330

Option 1)

165

Incorrect option

Option 2)

190

Incorrect option

Option 3)

255

Incorrect option

Option 4)

330

Correct option

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