Answer:
100
Step-by-step explanation:
We have the sum of first n terms of an AP,
Sn = n/2 [2a+(n−1)d]
Given,
36= 6/2 [2a+(6−1)d]
12=2a+5d ---------(1)
256= 16/2 [2a+(16−1)d]
32=2a+15d ---------(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S10 = 10/2 [2(1)+(10−1)2]
S10 =5[2+18]
S10 =100
This is the sum of the first 10 terms.
Hope it will help.
Answer:
-600
Step-by-step explanation:
The rate of change of a function f(x) in a certain interval
is the ratio between the change of the function and the change in the value of x:

The rate of change of a function tells how much the value of the function is changing per change in unit of x: therefore, for a linear function it corresponds to the slope of the line.
In this problem, the function f(x) is equal to the value of the business machine in dollars, while the variable x represents the number of years.
Here we are told that the machine was purchased for

while its value decreases by $600 each year, so

This means that the linear function that represents the value of the machine after x years is:

Therefore, the rate of change of the function is -600.