Question

If "f(x)=3-4x" .Find "sum_(r=1)^(10)f(r)​

Answer 1

GIVEN :

If f(x)=3-4x .Find $\sum_{r=1}^{10}f(r)$​

TO FIND :

The value of the $\sum_{r=1}^{10}f(r)$​

SOLUTION :

Given that the function f is defined by f(x)=3-4x

Now the expand the given sum as below:

$\sum_{r=1}^{10}f(r)$​

$=f(1)+f(2)+f(3)+f(4)+f(5)+f(6)+f(7)+f(8)+f(9)+f(10)$

For the values f(1), f(2), f(3), ..., f(10) substitute the values for x in the given function f(x)=3-4x for x=1,2,3,...,10

f(x)=3-4x

Put x=1,

f(1)=3-4(1)

=3-4

∴ f(1)=-1

Put x=2,

f(2)=3-4(2)

=3-8

∴ f(2)=-5

Put x=3,

f(1)=3-4(3)

=3-12

∴ f(3)=-9

Similarly we have f(4)=-13, f(5)=-17, f(6)=-21, f(7)=-25, f(8)=-29, f(9)=-33 and f(10)=-37

Substituting the values in the series we get,

$\sum_{r=1}^{10}f(r)=f(1)+f(2)+f(3)+f(4)+f(5)+f(6)+f(7)+f(8)+f(9)+f(10)$

$=-1+(-5)+(-9)+(-13)+(-17)+(-21)+(-25)+(-29)+(-33)+(-37)$

$=-1-5-9-13-17-21-25-29-33-37$

$=-190$

$\sum_{r=1}^{10}f(r)=-190$

∴ the value of the given sum $\sum_{r=1}^{10}f(r)$ is -190