Limit Point of a Sequence

In this article, we will discuss the limit point of a sequence. A set of numbers said to be a limit point of a sequence. It has two types of sequences.

1. Arithmetic sequence and

2. Geometric sequence.

Arithmetic sequence means that, the sequence of a numbers such that the difference between two consecutive members of the sequence is a constant. Geometric sequence means that, the sequence of a numbers such that the ratio between two consecutive members of the sequence is a constant. The limit point of a sequence formulas and example problems are given below.

Formulas and Example Problems for Limit Point of a Sequence

Sequences formulas are given below.

Formula for arithmetic sequence:

nth term of the sequence : an = a1 + (n - 1)d

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

Formula for geometric sequence:

nth term of the sequence: an = a1 * rn-1

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


Example problem 1:

Find the 11th term of the given series 11, 12, 13, 14, 15,......

Solution:

First term of the series, a1 = 11

Difference of two consecutive terms, d = 12 - 11 = 1

n = 11

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

So, the 11th term of the series  11, 12, 13, 14, 15,... = 11 + (11 - 1) 1

= 11 + 10 * 1

= 11 + 10

After simplify this, we get

= 21

So, the 11th term of the sequence 11, 12, 13, 14, 15,... is 21.

More Example Problems for Limit Point of a Sequence

Example problem 2:

Find out the 5th term of a geometric sequence if a1 = 70 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_5` as follows

`a_5 = a_1 * r^(5-1)`

= 70 * (2)4

= 70 * 16

After simplify this, we get

= 1120.

The 5th term of a geometric sequence is 1120.

The above examples are helpful to study of limit point of a sequence.