# How do you write a rule for the nth term given 28, 128, 228, 328, ...?

May 6, 2016

${n}^{t h}$ term of the series is $100 n - 72$
The series $28 , 128 , 228 , 328 , \ldots$ is arithmetic series whose first term $a$ is $28$ and difference between a term and its preceding term $d$ is $100$.
${n}^{t h}$ term of an arithmetic series whose first term is $a$ and common difference is $d$ is $a + \left(n - 1\right) d$.
Hence for above series it is $28 + \left(n - 1\right) 100 = 28 + 100 n - 100 = 100 n - 72$