The initial term of an arithmetic sequence is 5. The eleventh term is 125. what is the common difference of the arithmetic sequence?
a = 5
a + 10d = 125
5 + 10d = 125
10d = 120
d = 12
12
5 + (12 x 10)
5+120
125
Multiply by 12, ten times, then add 5 to get your 11th term.
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To find the common difference of an arithmetic sequence, we need to find the difference between any two consecutive terms.
Given that the initial term is 5, we can calculate the eleventh term by using the formula for the nth term of an arithmetic sequence:
nth term = (first term) + (n - 1) * (common difference)
In this case, the eleventh term is 125, so we have:
125 = 5 + (11 - 1) * d
120 = 10d
To find the common difference, we divide both sides of the equation by 10:
120/10 = 10d/10
12 = d
Therefore, the common difference of the arithmetic sequence is 12.