Question

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Q : How To find Nth term in number pattern.​

Answer 1

Step-by-step explanation:

Constant Difference Sequences

This is when the difference between terms is always the same.

e.g. 1, 4, 7, 10, ... This has a difference which is always 3.

find the 'nth term' by using this formula:

nth term = dn + (a - d)

Where d is the difference between the terms, a is the first term and n is the term number.

e.g. 6, 11, 16, 21, ...For this sequence d = 5, a = 6

So the formula is nth term = 5n + (6 - 5)

which becomes nth term = 5n + 1

Changing Difference Sequences

formula is

nth term = a + (n - 1)d + ½(n - 1)(n - 2)c

This time there is a letter c which stands for the second difference (or the difference between the differences and d is just the difference between the first two numbers.

eg, 2, 3, 6, 11, 18....

Here the difference between the first two numbers is 1 so d = 1

Also the second differences are 2 so c = 2 The first term is 2 so a = 2

Using the formula, nth term = 2 + (n - 1)x1 + ½(n - 1)(n - 2)x2

Getting rid of brackets (and noticing that ½ x 2 = 1):

nth term = 2 + n - 1 + n2 - 3n + 2

Simplifying,

nth term = n2 - 2n + 3