What is the explicit formula for the arithmetic sequence?

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erlent00s · Accepted Answer

To obtain the nth term of a Sequence we derive Explicit formula.
For, Arithmetic Sequence
A sequence in which difference between two consecutive terms is same, that is , A sequence

a_{1}, a_{2}, a_{3} . . . . . . . . . a_{n}

, Such that

a_{2} - a_{1} = a_{3} - a_{2} = . . . . . a_{n} - a_{n - 1} = d,

is an Arithmetic Sequence.
To Derive the Explicit Formula ,The following sequence can be written as:

a_{1} = a a_{2} = a + (2 - 1) d = a + d a_{3} = a + (3 - 1) d = a + 2 d a_{4} = a + (4 - 1) d = a + 3 d a_{5} = a + (5 - 1) d = a + 4 d a_{6} = a + (6 - 1) d = a + 5 d a_{7} = a + (7 - 1) d = a + 6 d

.......................
......................

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

This is Required explicit formula for the arithmetic sequence.

What is the explicit formula for the arithmetic sequence?

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