Question

What is the explicit formula for the arithmetic sequence?

Answer 1

Mathwords: Arithmetic Sequence. A sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n.

Answer 2

Answer with explanation:

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

  $a_{1},a_{2},a_{3},.................a_{n},\text{Such that}\\\\a_{2}-a_{1}=a_{3}-a_{2}=.....a_{n}-a_{n-1}=d$,

is an Arithmetic Sequence.

To Derive the Explicit Formula ,The following sequence can be written as:

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

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

This is Required explicit formula for the arithmetic sequence.