Question

Find the sum of the summation of 2 i minus 9, from i equals 3 to 10.

Answer 1

Sum = 32

Explanation:

We are given the following data and we are to find its sum:

`\sum _(i=3)^(10) 2i-9`

Sum: S

`S = [ 2 ( 3 ) - 9 ] + [ 2 ( 4 ) - 9 ] + [ 2 ( 5 ) - 9 ] + [ 2 ( 6 ) - 9 ] + [ 2 ( 7 ) - 9 ] + [ 2 ( 8 ) - 9 ] + [ 2 ( 9 ) - 9 ] + [ 2 ( 1 0 ) - 9 ]`

`S=2(3+4+5+6+7+8+9+10)-8(10)`

`S=2(52)-72`

`S=104-72`

S = 32

Answer 2

`\sum_3^(10)(2i-9) =32`

Explanation:

First we write the problem in summation notation.

The sum of the summation of 2 i minus 9, from i equals 3 to 10 is:

`\sum_3^(10)(2i-9)`

Now we solve the expression

`\sum_3^(10)(2i-9) = (2(3) -9) + (2(4) -9) + (2(5)- 9) + (2(6) -9) +(2(7) -9)+\\\\(2(8) -9)+ (2(9) -9)+ (2(10) -9)\\\\\\\sum_3^(10)(2i-9) = (6 -9) + (8 -9) + (10- 9) + (12 -9) +(14 -9)+ (16 -9)+\\\\(18 -9)+ (20 -9)\\\\\\\sum_3^(10)(2i-9) = (-3) + (-1) + (1) + (3) +(5)+ (7)+ (9)+ (11)\\\\\\\sum_3^(10)(2i-9) =32`