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]
Answer:
Step-by-step explanation:
Please find the attachment.
We have been given that a container is shaped like a triangle prism. Each base of container is an equilateral triangle with each side 6 cm. The height of container is 15 cm.
To find the lateral surface area of our given container we will use lateral surface area formula of triangular prism.
, where, a, b and c represent base sides of prism and h represents height of the prism.
Upon substituting our given values in above formula we will get,
Therefore, lateral surface area of our given container is 270 square cm.
Answer:
C
Step-by-step explanation:
We can use process of elimination
D is incorrect because the roots are 3 and -4 and there are no negative roots visible
B is wrong because the roots -3 and -6 are both negative
You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6
For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate
Answer:
12.78
Step-by-step explanation:
63.65 divided by 5 = 12.7
