Question

What is the 59th term in the sequence? {21, 14, 7, 0...}

Answer 1

Answer:

Step by Step Solution



0,7,14,21

Your input 0,7,14,21 appears to be an arithmetic sequence

Find the difference between the members

a2-a1=7-0=7

a3-a2=14-7=7

a4-a3=21-14=7

The difference between every two adjacent members of the series is constant and equal to 7

General Form: an=a1+(n-1)d

an=0+(n-1)7

a1=0   (this is the 1st member)

an=21  (this is the last/nth member)

d=7  (this is the difference between consecutive members)

n=4  (this is the number of members)

Sum of finite series members

The sum of the members of a finite arithmetic progression is called an arithmetic series.

Using our example, consider the sum:

0+7+14+21

This sum can be found quickly by taking the number n of terms being added (here 4), multiplying by the sum of the first and last number in the progression (here 0 + 21 = 21), and dividing by 2:

n(a1+an)2

4(0+21)

     2

The sum of the 4 members of this series is 42

This series corresponds to the following straight line y=7x+0