# How do you find an equation that describes the sequence 4, 8, 12, 16,... and find the 13th term?

Feb 27, 2017

${T}_{13} = 52$

#### Explanation:

This sequence is an arithmetic progression because
${T}_{2} - {T}_{1} = {T}_{3} - {T}_{2} = {T}_{4} - {T}_{3} = d = 4$, where d = common difference.

For arithmetic progression,
${T}_{n} = a + \left(n - 1\right) d$, where $a =$first term, n = number of term.

Therefore,
${T}_{13} = 4 + \left(13 - 1\right) \cdot 4$

${T}_{13} = 4 + \left(12\right) \cdot 4$

${T}_{13} = 4 + 48 = 52$