If 'd' is the common difference between the two consecutive terms of AP,

d = t_{2} - t_{1}
n^{th} term of A.P

t_{n} = a + (n-1)d

To find the nth term of Fibonacci sequence is

t_{n} = t_{n-2} + t_{n-1}.

We can build a sequence if the nth term is given.

2. To find the nth term of a sequence:

If the terms in a sequence go up by a same number for each term, then the number will appear multiplied by n times in the formula for the nth term of the sequence.

Example:

Find the formula to find the nth term of the sequence

7, 11, 15, 19,....

Solution: Here t₁ = 7

t₂ = 11

t₃ = 15

t₄ = 19 and so on.

The common difference is

t₄ - t₃ = t₃ - t₂ = t₂- t₁ = d

19 - 15 = 15 - 11 = 11- 7 = 4

So each term of this sequence go up by 4.

4n sequence : 4, 8, 12, 16, .....

The given sequence is

7, 11, 15, 19, ....

So to get the given sequence, let us add 3 for each term.

We had seen some examples in this page, 'Sequence-II' . We will see more examples in the next page.

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