Sequence Comparison

In this article, we will discuss about the sequence comparison. It has two types of sequences. One is arithmetic sequence and next one is geometric sequence. Arithmetic sequence means that, the sequence of numbers such that the difference between two consecutive members of the sequence is a constant. Geometric sequence means that, the sequence of numbers such that the ratio between two consecutive members of the sequence is a constant. The sequence comparison formulas and example problems are given below.

I like to share this Sequence and Series with you all through my article.

Formulas for Sequence Comparison:

Compare the formulas for arithmetic and geometric sequences.

Formula for arithmetic sequence:

nth term of the sequence : a_n = a_1 + (n - 1)d

Series of the sequence: S_n = (n(a_1 + a_n))/2

Formula for geometric sequence:

nth term of the sequence: a_n = a_1 * r^(n-1)

Series of the sequence: S_n = (a_1(1-r^n))/(1 - r)

Example Problems for Sequence Comparison:

We will compare the arithmetic and geometric sequence problems.

Example problem 1:

Find the 24th term of the given series 14, 16, 18, 20,....

Solution:

First term of the series, a1 = 14

Difference of two consecutive terms, d = 16 - 14 = 2

n = 24

The formula to find the nth term of an arithmetic series, a_n = a_1 + (n-1)d

So, the 24th term of the series 14, 16, 18, 20,.... = 14 + (24 - 1) 2

= 14 + 23 * 2

= 14 + 46

After simplify this, we get

= 60

So, the 24th term of the sequence 14, 16, 18, 20,... is 60

My forthcoming post is on prime numbers to 100 chart and Area of a Trapezoid will give you more understanding about Algebra.

Example problem 2:

Find out the 15th term of a geometric sequence if a1 = 15 and the common ratio (C.R) r = 2

Solution:

Use the formula a_n = a_1 * r^(n-1) that gives the nth term to find a_15 as follows

a_15 = a_1 * r^(15-1)

= 15 * (2)14

= 15 * 16384

After simplify this, we get

= 245760

The 15th term of a geometric sequence is 245760.

The above examples are helpful to study of sequence comparison.