Arithmetic Sequences: Practice

The first term is the term in position $1$, the number written at the start of the list.

$a_1 = 6$

The value $4$ is the common difference and $10$ is the second term, not the first.

The common difference is any term subtracted from the term that follows it.

$d = 10 - 6 = 4$

Every gap in the list is the same $4$, which is what makes the sequence arithmetic.

The subscript $4$ means the term in position $4$. Count in from the start: $3$ is first, $8$ is second, $13$ is third, $18$ is fourth.

$a_4 = 18$

Each term is the one before it plus the common difference $d = 4$. Add $4$ to the last term shown.

$18 + 4 = 22$

The subscript is a position counter, not a value or a difference. The $3$ in $a_3$ marks where the term sits.

$a_3 = \text{the 3rd term}$

A common difference of $-2$ means each term is $2$ less than the one before it, so the list decreases.

$7 - 9 = -2$

Only $9, 7, 5, 3$ steps down by $2$; the others step up by $2$.

The subscript $5$ asks for the term in position $5$, the fifth number in the list.

$a_5 = 14$

The second term is the first term plus the common difference. Here $d = -10$, so the term drops.

$a_2 = 100 + (-10) = 90$

The first term already sits in position $1$ with no steps taken. Reaching position $6$ takes $n - 1$ steps.

$6 - 1 = 5$

Use $a_n = a_1 + (n-1)d$ with $n = 4$, so there are $3$ steps of size $3$.

$a_4 = -5 + 3\times 3 = 4$

Count to position $3$: $6$ is first, $10$ is second, $14$ is third.

$a_3 = 14$

The common difference is $d = 25 - 30 = -5$, so add $-5$ to the last term shown.

$15 + (-5) = 10$