sequences | Sophia's Blog

This week, we worked with arithmetic sequences.

2,4,6,8,10…

Each of the numbers above are considered terms. The number 2 is considered $t_1$

Part 1:

When finding a term, we use the formula: $t_n$ = $t_1$ + (n-1)d (d represents difference between terms.)

For finding term 50, we will use this formula.

$t_{50}$ = 2 + (50-1)2

$t_{50}$ = 2 + 98

$t_{50}$ = 100

Part 2:

When finding the sum of all terms, we use the formula: $s_{50}$ = $\frac {n}{2}$ + ( $t_1$ + $t_n$ )

I will be using the same sequence from above to find the sum.

$s_{50}$ = $\frac {50}{2}$ + ( 2 + 50)

$s_{50}$ = 25+ 52

$s_{50}$ = 77

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