POSITION TO TERM RULE

Problem 1 :

1) For each question use the rule to find the first five terms of the sequence.

2) Can you find the 10^th term of the sequence ?

3) Can you find the 100^th term of the sequence ?

Rule :

2n - 1

Solution :

Given rule = 2n - 1

1^st term = 1, 2^nd term = 3, 3^rd term = 5, 4^th term = 7 and 5^th term = 9

10^th term :

= 2(10) - 1

= 20 - 1

= 19

100^th term :

= 2(100) - 1

= 200 - 1

= 199

Problem 2 :

Write the term to term rule for the sequence given below, then work out the next two terms.

4, 9, 14, 19, 24, .......

a) Is the number 37 in the sequence.

Solution :

4, 9, 14, 19, 24, .......

Every term is added with 5, by creating the rule

a_n = 5n - 1

Finding next two terms :

The next two terms are 24 and 29.

a) Is 34 in the sequence :

Since we don't know whether 34 is in the sequence or not, we can consider a_n = 34

34 = 5n - 1

5n = 34 + 1

5n = 35

n = 35/5

n = 7

From this, it is clear 7^th term of the sequence is 34.

Problem 3 :

Calculate the difference between the 10^th term and 50^th term of the sequence

9, 14, 19, 24, ... ...

Solution :

9, 14, 19, 24, ... ...

In every term 5 is added. Creating the general term, we get

a_n = 5n + 4

Problem 4 :

Find the n^th term for each of the following sequences

1/2, 3/4, 5/6, 7/8, .............

Solution :

By observing each values in the numerator and denominator, numerators are odd values and denominators are even numbers.

Odd values = 2n - 1

Even values = 2n

So, n^th term of the sequence is (2n - 1)/2n