Worksheet: Arithmetic Series

An arithmetic series is the sum of the terms of an arithmetic sequence. In this worksheet, practice calculating a given arithmetic series.

Q1:

Find the sum of the first 17 terms of the arithmetic series .

Q2:

Find the sum of the first 26 terms of the arithmetic series .

Q3:

Find the sum of the arithmetic series .

Q4:

Find, in terms of , the sum of the arithmetic sequence .

Q5:

Find the sum of the 6 consecutive terms that start from the eighteenth term of the arithmetic series .

Q6:

Find the number of terms in the arithmetic sequence whose first term is 11 and last term is 81, where the sum of all the terms is 506.

Q7:

Find the number of terms for which the sum of the sequence is 0.

Q8:

Find the least number of terms needed to make the sum of the arithmetic sequence negative.

Q9:

Find the sum of the sequence of odd natural numbers which are greater than 46 and less than 92.

Q10:

Find the sum of the second half of terms of the sequence .

Q11:

Find the 12-term arithmetic sequence given the sum of the first 4 terms is and the sum of the last 4 terms is .

Q12:

Find the arithmetic sequence given the sum starting from the second term is 567, the sum excluding the last term is 469 and the difference between the tenth and sixth terms is 28.

Q13:

Find the arithmetic sequence that starts at given that the sum of the first 17 terms is 748 and the arithmetic mean between and is 48.

Q14:

Find all possible arithmetic sequences that satisfy and where is the sum of the first terms of the arithmetic sequence, is the term, and is the first term.

A or
B or
C or
D or

Q15:

In an arithmetic sequence that starts at , and the sum of the eighth and the twelfth terms exceeds the fifteenth by 7. Find the number of terms whose sum is 322.

Q16:

Find the sum of a sequence which has 21 terms, given that the sum of the first third of the terms is 21 and that of the last third of the terms is . Then, find the sum of the middle five terms.

Q17:

14 pegs are placed on a washing line at 7 meters apart with a basket beside the first peg. Find the total distance covered if a person collects the pegs one by one, without moving the basket and returning to the basket after collecting each peg.

Q18:

A theater has 40 rows of seats where the first row has 27 seats and each subsequent row has 3 more seats than the one previous. Find the total number of seats in the theater.

A
3 540
B
3 480
C
3 393
D
3 420
E
6 840

Q19:

The house numbers on one side of a street are . Find the house number where the sum of the numbers before it is equal to the sum of the numbers after it.

Q20:

A runner is practicing for a long-distance race. He covers 6 km on the first day and then plans to increase his distance by 0.7 km every day. In how many days will the runner cover a distance of 67.6 km given he follows the plan?