First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an

S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)

S=an+an−1+an−2+an−3+...+a1

S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)

Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2S=n(a1+an)
S=n/2(a1+an)

Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]

5 0

3 years ago

8x2 - 6x + 3 – 2x – 10x?

Marina CMI [18]

Answer:

8 $x^{2}$ + 3 + -6x

Step-by-step explanation:

First we need to find the like terms so that we could add them. In this case the like terms are,

1. 6x , -2x , -10x

So, these are the only terms that we can add in this expression.

Hence,

=> 8 $x^{2}$ + 3 + (6x - 2x - 10x)

=> 8 $x^{2}$ + 3 + -6x

And this is as simple as this expression can go until we find the value of "x" which is not yet told.

Hope my answer helped.

4 0

3 years ago

Read 2 more answers

Simplify<br> (a+3)2 -3 (2a+3)

Anna71 [15]

Answer:

-4a-3

Step-by-step explanation:

$2a + 6 - 6a - 9 = - 4a - 3$

5 0

3 years ago

4 in.

sleet_krkn [62]

Answer:

305.12 square inches

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The area of the window is equal to the area of a rectangle, plus the area of two quarter circles plus the area of the smaller square between the two upper corners

Find the area of rectangle

$A=(12)(26-4)=264\ in^2$