Question

the first three terms of a sequence are given round to the nearest thousandth(if necessary). 413,405,397,...Find the 48th term

Answer 1

37

1) Examining the sequence we can notice that

413-405 = 8

405 -397 =8

So, this is an Arithmetic Sequence whose common difference is -8

2) Therefore, we can write one Explicit Formula so that we can find out the 48th term

$\begin{gathered} a_n=a_1+(n-1)d \\ a_{48}=413+(48-1)(-8) \\ a_{48}=413\text{ +47(-8)} \\ a_{48}=413+(-376) \\ a_{48}=413-376\text{ =37} \end{gathered}$

3) Hence, the 48th term of that Arithmetic Sequence is 37