Week 1: Arithmetic Sequence

$t_n$ $t_{50}$ $\frac {n}{2}$

Question: We have an arithmetic sequence of… -1.5, 2.75, 7, 11.25, 15.5…. Find $t_{50}$ and give the general equation for $t_n$ .

First, we have to see what the question gives us:

$t_1 = -1.5$ ** $t_1 =$ the first term in the sequence

$d = 2.75 -(-1.5)$

$d = 4.25$ ** $d =$ common difference between the term

$t_{50} = ?$

Find the $t_{50} =$

$t_{50} =$ (-1.5) + (50-1)4.25

$t_{50} =$ (-1.5) + (49)4.25

$t_{50} =$ (-1.5) + 208.25

$t_{50} =$ 206.75

Find the general equation for the sequence:

$t_n =$ (-1.5) + (n – 1)4.25

$t_n =$ (-1.5) + 4.25n -4.25

$t_n =$ 4.25n -5.75

Find the sum of these first 50 terms in the sequence:

$Sn_n =$ $\frac {n}{2}$ ( $t_{1}$ + $t_n$ )

$Sn_{50} =$ $\frac {50}{2}$ ( -1.5 + 206.75)

$Sn_{50} =$ 25 (205.25)

$Sn_{50} =$ 5131.25