## ARITHMETIC SERIES WORKSHEET

In this page arithmetic series worksheet you are going to see practice questions of the topic arithmetic series. You can find answer for each questions in the page below.

 Questions Solution (1) Find the sum of first (i) 75 positive integers (ii) 125 natural numbers (2) Find the sum of first 30 terms of an A.P whose nth term is 3 + 2 n arithmetic series worksheet (3) Find the sum of each arithmetic series (i) 38 + 35 + 32 + .......... + 2(ii) 6 + 5 ¼ + 4 ½ + ......... 25 terms Solution (4) Find the sum of each arithmetic series described(i) a = 5  n = 30 and L = 121(ii) a = 50    n = 25    and d = -4 Solution (5) Find the sum of first 40 terms of the series 1² - 2² + 3² - 4²  + ........ Solution (6) In an arithmetic series,the sum of first 11 terms is 44 and the that of the next 11 terms is 55. Find the arithmetic series. Solution (7) In an arithmetic sequence 60,56,52,48,....... starting from the first term,how many terms are needed so that  their sum is 368? Solution (8) Find the sum of all 3 digit natural numbers,which are divisible by 9. Solution (9) Find the sum of first 20 terms of the arithmetic series in which 3 rd term is 7 and 7th term is 2 more than three times its 3rd term. Solution (10) Find the sum of all natural numbers between 300 and 500 which are divisible by 11. Solution (11) Solve 1 + 6 + 11 + 16 + ..........  + x = 148 Solution (12) Find the  sum of all natural numbers between 100  and 200 which are not divisible by 5. Solution (13) A construction company will be penalized each day of delay in construction for bridge. The penalty will be \$4000 for the first day and will increase by \$10000 for each following day. Based on its budget, the company can afford to pay a maximum of \$ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed Solution (14) The sum of \$1000 is deposited every year at 8% simple interest. Calculate the interest at the end of each year. Do these interest amounts form an A.P?. If so,find the total interest at the end of 30 years. Solution (15) The sum of first n terms of a certain series is given as 3n² - 2n.Show that the series is an arithmetic series. Solution (16) If a clock strikes once at 1'o clock,twice at 2'o clock and so on.How many times will it strike a day? Solution (17) Show that the sum of an arithmetic series whose first term is a,second term is b and the last term is c is equal to [(a+c) (b+c-2a)]/2(b-a) Solution (18) If there are (2n+1) terms in an arithmetic series,then prove that the ratio of the sum of odd terms to the sum of even terms is (n+1) : n Solution (19) The ratio of the sums of first m and first n terms of an arithmetic series is m²:n² show that the ratio of the m th and nth terms is (2m-1) :(2n-1) Solution (20) A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of 97 bricks. Each row must be decreased by 2 bricks on each end  and the construction should stop at 25th row. How many bricks does he need to buy? Solution 1. (i)  2850    (ii)   7875
2. 1020
3. (i)  260   (ii) -75
4. (i)  1890   (ii) 50
5. - 820
6. 39/11 + 40/11 + 41/11 + ...........
7. Sum of 8 or 23 terms of arithmetic sequence is  368.
8. 55350
9. 740
10. 7227
11. x = 36
12.  12000
13. 15
14. 37200
15. a = 1 d = 6
16. 156 times
17. hence proved
18. hence proved
19. hence proved
20. 1225 bricks

Sets and Functions

 Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4

Sequence and Series

MATRIX

 Exercise 4.2 Exercise 4.3

Coordinate Geometry

 Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5

Geometry

Trigonometry

Mensuration

Statistics

Exercise 11.1

Probability

These are the questions in the topic arithmetic series worksheet.arithmetic series worksheet

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