Sums - Series of Integers M to N - Equation to Sum

Level 2

This math topic covers the calculation of the sum of a series of consecutive integers between two given numbers \(M\) and \(N\) using a specific formula. The problems provide an equation in each case and require finding the correct sum from multiple choices. Each scenario uses this formula to subtract the sum of integers from 1 to \(M-1\) from the sum of integers from 1 to \(N\), effectively isolating the sum from \(M\) to \(N\). The advanced level of these problems suggests they enhance skills in arithmetic sequences and algebraic manipulation.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Sums - Series of Integers M to N - Equation to Sum

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


What is the sum of the integers from 7 to 22 based on this equation?

22(22+1)2(71)72\frac{22(22+1)}{2} - \frac{(7-1)7}{2}

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Sums - Series of Integers M to N - Equation to Sum Worksheet

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Math worksheet on 'Sums - Series of Integers M to N - Equation to Sum (Level 2)'. Part of a broader unit on 'Patterns and Sums - Advanced' Learn online: app.mobius.academy/math/units/patterns_and_sums_advanced/
1
What is the sum of the integers from 2 to 12 based on this equation?
A LaTex expression showing 12(12+1) over 2 - (2-1)2 over 2
a
75
b
65
c
77
d
90
e
78
2
What is the sum of the integers from 6 to 15 based on this equation?
A LaTex expression showing 15(15+1) over 2 - (6-1)6 over 2
a
110
b
121
c
90
d
105
e
99
3
What is the sum of the integers from 17 to 25 based on this equation?
A LaTex expression showing 25(25+1) over 2 - (17-1)17 over 2
a
172
b
215
c
164
d
189
e
205
4
What is the sum of the integers from 6 to 16 based on this equation?
A LaTex expression showing 16(16+1) over 2 - (6-1)6 over 2
a
121
b
105
c
138
d
115
e
126
5
What is the sum of the integers from 9 to 18 based on this equation?
A LaTex expression showing 18(18+1) over 2 - (9-1)9 over 2
a
135
b
117
c
143
d
126
e
154
6
What is the sum of the integers from 6 to 18 based on this equation?
A LaTex expression showing 18(18+1) over 2 - (6-1)6 over 2
a
175
b
150
c
138
d
161
e
156
7
What is the sum of the integers from 3 to 11 based on this equation?
A LaTex expression showing 11(11+1) over 2 - (3-1)3 over 2
a
60
b
63
c
65
d
52
e
75