1 answer

What is the sum of the arithmetic series: - 3 + 7 + 17 + ... + 57?

Question:

What is the sum of the arithmetic series: - 3 + 7 + 17 + ... + 57?

Answers

First find the relationship between the terms.

Explanation:

7 - (-3) = 10

Each term is 10 more than the previous.

Now, we must find the number of terms

Plugging in 57 for #t_n#, 10 for r and -3 for a. We are solving for n.

#t_n# = a + (n - 1)r

57 = -3 + 10n - 10

57 + 13= 10n

70 = 10n

7 = n

Now we can find the sum:

#s_n# =#(n/2)(t_1 + t_n)#

#s_n# = #7/2(-3 + 57)#

#s_n# = #3.5(54)#

#s_n# = 189

The sum is 189

.

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