How do you find the sum of the arithmetic series #7+14+21+28+...+98#?

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Answer 1 · 2016-10-17T22:17:58

The sum is #735#.

We need to start by finding the number of terms, #n#.

The formula #t_n = a + (n - 1)d# gives the nth term of an arithmetic series.

#98 = 7 + (n - 1)7#

#98 = 7 + 7n - 7#

#7n = 98#

#n = 14#

We can now apply the formula #s_n = n/2(t_1 + t_n)# to determine the sum of the series.

#s_14 = 14/2(7 + 98)#

#s_14 = 7(105)#

#s_14 = 735#

Hopefully this helps!