Use
S=n2 to find the sum of 1+3+5+. . . + 301.

I'm not sure what the question means by "use S = n^2"...

At any rate, the given sum

1 + 3 + 5 + … + 301

is simply the sum of the first 151 odd positive integers, which we can write in the form 2n - 1 for n between 1 and 151. That is,

We can expand the sum as

Next, recalling that

it follows that

(Probably "S = n^2" means "sum of n odd integers = n ²")

b. x- 48 =120

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form