Given:
The first two terms in an arithmetic progression are -2 and 5.
The last term in the progression is the only number in the progression that is greater than 200.
To find:
The sum of all the terms in the progression.
Solution:
We have,
First term : 
Common difference : 


nth term of an A.P. is

where, a is first term and d is common difference.

According to the equation,
.



Divide both sides by 7.

Add 1 on both sides.

So, least possible integer value is 30. It means, A.P. has 30 term.
Sum of n terms of an A.P. is
![S_n=\dfrac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Substituting n=30, a=-2 and d=7, we get
![S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]](https://tex.z-dn.net/?f=S_%7B30%7D%3D%5Cdfrac%7B30%7D%7B2%7D%5B2%28-2%29%2B%2830-1%297%5D)
![S_{30}=15[-4+(29)7]](https://tex.z-dn.net/?f=S_%7B30%7D%3D15%5B-4%2B%2829%297%5D)
![S_{30}=15[-4+203]](https://tex.z-dn.net/?f=S_%7B30%7D%3D15%5B-4%2B203%5D)


Therefore, the sum of all the terms in the progression is 2985.
Answer:

Step-by-step explanation:
Let's solve for C.

Step 1: Flip the equation.

Step 2: Add
to both sides.


Step 3: Divide both sides by
.


Answer:


Differentiate both sides wrt
:

By the chain rule, we get


Solve for
:


Combine like terms
-7y² + 6y² - 2y² = -3y²
4y + (-5y) - (-9y) = 4y - 5y + 9y = 8y
9 + 9 - (-2) = 9 + 9 + 2 = 20
-3y² + 8y + 20 is your answer
hope this helps
Answer: 
Step-by-step explanation:
Confidence interval for population mean is given by :-
(1)
, where
= Sample mean
= Critical z-value
= Population standard deviation.
n= Sample size.
As per given , we have
n= 610

Significance level for 85% confidence : 
By z-table critical two tailed z-value : 
Put all values in (1) , we get




Hence, the 85% confidence interval for the mean consumption of meat among people over age 40. = 