Write a rule for the nth term of the arithmatic sequence. Then find a10.
1. -4,2,8,14,20
2. -25,-29,-30,-37,-41
#1 +6
#2 ???
To find the nth term of an arithmetic sequence, you can use the formula:
an = a1 + (n - 1)d
where:
an = the nth term
a1 = the first term
n = the position of the term in the sequence
d = the common difference between consecutive terms
Let's apply this formula to the given sequences:
1. -4, 2, 8, 14, 20:
In this sequence, the first term (a1) is -4, and the common difference (d) between consecutive terms is 2 - (-4) = 6.
Substituting these values into the formula, we get:
an = -4 + (n - 1)6
To find a10, we substitute n = 10 into the formula:
a10 = -4 + (10 - 1)6
a10 = -4 + 54
a10 = 50
Therefore, a10 in the sequence -4, 2, 8, 14, 20 is equal to 50.
2. -25, -29, -30, -37, -41:
In this sequence, the first term (a1) is -25, and the common difference (d) between consecutive terms is -29 - (-25) = -4.
Substituting these values into the formula, we get:
an = -25 + (n - 1)(-4)
To find a10, we substitute n = 10 into the formula:
a10 = -25 + (10 - 1)(-4)
a10 = -25 + 9(-4)
a10 = -25 - 36
a10 = -61
Therefore, a10 in the sequence -25, -29, -30, -37, -41 is equal to -61.