Explicit Formula Calculator

Calculate nth Term







Formula

The formula to calculate the nth term of an arithmetic sequence is:

\[ a_n = a_1 + (n - 1) \cdot d \]

The formula to calculate the nth term of a geometric sequence is:

\[ a_n = a_1 \cdot r^{(n - 1)} \]

Where:

Example

For an arithmetic sequence with \( a_1 = 2 \), \( d = 3 \), and \( n = 5 \):

\[ a_5 = 2 + (5 - 1) \cdot 3 = 2 + 12 = 14 \]

For a geometric sequence with \( a_1 = 2 \), \( r = 3 \), and \( n = 5 \):

\[ a_5 = 2 \cdot 3^{(5 - 1)} = 2 \cdot 81 = 162 \]

What is an Explicit Formula?

An explicit formula allows you to find the nth term of a sequence directly, without needing to know the previous terms. It is particularly useful for arithmetic and geometric sequences.