Question

Find the 52nd term.29, 229, 429, 629,…

Answer 1

1. Find the common difference (d): subtract each term from the previous term:

$\begin{gathered} 229-29=200 \\ 429-229=200 \\ 629-429=200 \end{gathered}$

Common difference: d=200

2. Find the formula of the sequence:

$a_n=a_1+d(n-1)$

a1 is the first term

d is the common diffference

$\begin{gathered} a_n=29+200(n-1) \\ a_n=29+200n-200 \\ a_n=200n-171 \end{gathered}$

3. Find 52nd term

n=52

$\begin{gathered} a_{52}=200(52)-171 \\ a_{52}=10400-171 \\ a_{52}=10229 \end{gathered}$

Then, the 52nd term is 10,229