If the first term in an arithmetic series is 42 and the tenth term is 78 , what is the fifth term of the series
To find the common difference, subtract the first term from the tenth term: 78 - 42 = <<78-42=36>>36.
To find the fifth term, add the common difference four times, because the fifth term is four terms away from the first term: 42 + (36 * 4) = 42 + 144 = <<42+(36*4)=186>>186. Answer: \boxed{186}.
To find the fifth term of an arithmetic series, we need to determine the common difference (d) first.
Using the formula for the nth term of an arithmetic series:
an = a1 + (n - 1)d
where:
an = nth term
a1 = first term
d = common difference
Given:
a1 = 42
n = 10
an = 78
We can rearrange the formula to solve for d:
an = a1 + (n - 1)d
78 = 42 + (10 - 1)d
78 = 42 + 9d
36 = 9d
d = 36 / 9
d = 4
Now that we know the common difference (d = 4), we can find the fifth term:
a5 = a1 + (5-1)d
a5 = 42 + (4)d
a5 = 42 + 4(4)
a5 = 42 + 16
a5 = 58
Therefore, the fifth term of the series is 58.