Find the sum of the arithmetic progression 1,4,7,10,13,16 .Every third term of the above progression is removed i. e 7,16. Find the sum of the remaining terms

The sum of the arithmetic progression is 51

The sum of the remaining terms is 28

Step-by-step explanation:

Sum of terms of an arithmetic progression

Being a1 the first term of an arithmetic progression, an its last term, and n the number of terms, the sum of all terms is calculated as:

We are given the progression:

1,4,7,10,13,16

We need to check if the list of numbers is a progression. The difference between consecutive terms must be equivalent.

Since:

4 - 1 = 3

7 - 4 = 3

10 - 7 = 3

And the rest of the differences also result in 3, the series of numbers has a common difference of 3.

The progression has the following parameters:

a1=1, an=16, n=6

Let's find the sum:

The sum of the arithmetic progression is 51

If we removed the terms 7 and 16, the new sum is:

51 - 7 - 16 = 28

The sum of the remaining terms is 28

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368