# What is the recursive formula for this sequence: 100,160, 226, 298.6,.. ?

Apr 13, 2016

It is explained below

#### Explanation:

Letting  a_1=100; a_2=160, the recursive formula works out as follows:

${a}_{3} = {a}_{2} + \left({a}_{2} - {a}_{1}\right) + \frac{{a}_{2} - {a}_{1}}{10} = \frac{21}{10} {a}_{2} - \frac{11}{10} {a}_{1}$

${a}_{4} = {a}_{3} + \left({a}_{3} - {a}_{2}\right) + \frac{{a}_{3} - {a}_{2}}{10} = \frac{21}{10} {a}_{3} - \frac{11}{10} {a}_{2}$

and in general
${a}_{n + 1} = \frac{21}{10} {a}_{n} - \frac{11}{10} {a}_{n - 1}$ for n>=2