Question

Express the series 19+23+27 +31 + 35+ 39 +43 + 47 using sigma notation.

Answer 1

8

∑ 15+4n

n=1

264

Explanation:

The difference between all of the terms is 4, so you need to find a way to form that into your equation. 19-4=15, so you would use that for the first part of the equation. Since all of the following answers have a difference of 4 each time, you would need to multiply 4 by n and then add them to 15 to get your resulting answers. Since in the first term 4 is being multiplied by 1, n=1, and since there are 8 terms in the series given, you would put the 8 on top of the sigma symbol.

To get 264, you would add all of the numbers in the series together.

Answer 2

Answer: 135

Explanation:

Find the difference between the members. The difference between every two adjacent members of the series is constant and equal to 4. The sum of thUsing our example, consider the sum. This sum can be found quickly by taking the number of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 19 + 35 = 54), and The sum of the 5 members of this series is 135 dividi This series corresponds to the following straight line y=4x+19ng by 2. Of a finite arithmetic progression is called an arithmetic series.