# What is the 24th term of an arithmetic sequence where a1=8 and a9= 56?

May 9, 2016

$56 = 8 + \left(9 - 1\right) d$

$48 = 8 d$

$6 = d$

The common difference is of $6$. We can now find the 24th term using the formula ${t}_{n} = a + \left(n - 1\right) d$

${t}_{24} = 8 + \left(24 - 1\right) 6$

${t}_{24} = 146$

Thus, the 24th term is $146$.

Hopefully this helps!