The sum of the arithmetic series 4+9+14+19+24+ . . . . . . . +99 is S(20) = 1030
The given series:
4+9+14+19+24+ . . . . . . . +99
We can conclude:
a(1) = 4
a(n) = 99
d = 9 - 4 = 5
Step 1.
Find n using the formula of nth term.
a(n) = a(1) + (n-1) . d
99 = 4 + (n -1). 5
99 = 5n - 1
5n = 100
n = 20
Step 2.
Find the sum for the n terms using the sum formula of an arithmetic series:
S(n) = n/2 (a(1) + a(n))
Substitute n = 20, a(1) = 4, and a(20) = 99
S(20) = 20/2 . (4 + 99)
= 10 . 103 = 1030
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