# ARITHMETIC SERIES PRACTICE WORKSHEET

Arithmetic Series Practice Worksheet :

This section will contain set of questions using the concept arithmetic series.

## Arithmetic Series Practice Worksheet - Practice questions

(1) Find the sum of the following APs

(i)  2 , 7 , 12,....... to 10 terms            Solution

(ii) -37, -33, -29,..................... to 12 terms

(iii) 0.6, 1.7, 2.8,............... to 100 terms

(iv) 1/15, 1/12, 1/10,................... to 11 terms

(2) Find the sums given below

(i) 7 + 10 (1/2) + 14 + ...............+ 84

(ii) 34 + 32 + 30 + .................. + 10

(iii)  - 5 + (-8) + (-11) + .............+ (-230)

(3) In an AP

(i) Given a = 5, d = 3, an = 50 find n and Sn

(ii) Given a = 7, a13 = 35 find d and S13

(iii) Given a12 = 37 , d = 3 find a and S12

(iv) Given a3 = 15 , S10 = 125 find d and a10

(v) Given d = 5 , S9 = 75 find a and a9

(vi) Given a = 2 , d = 8, Sn = 90 find n and an

(vii) Given a = 8 , an = 62, Sn = 210 find n and d                    Solution

(viii) Given an = 4, d = 2, Sn = -14 find n and a

(ix) Given a = 3, n = 8, Sn = 192 find d

(x) Given l = 28 , S = 144 , and there are total 9 terms. Find a

(4) How many terms of the AP 9, 17, 25,.......... must be taken to give a sum of 636?

(5) The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and common difference.

(6) The first and last term of an AP are 17 and 350 respectively.If the common difference is 9, how many terms are there and what is their sum?

(7) Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

(8) The sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

(9) If the sum of 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

(10) Show that a₁,a₂,............ an form an AP where an is defined as below

(i) a n = 3 + 4 n

(ii) a n = 9 - 5 n

Also find the sum of 15 terms in each case.

(11) If the sum of the first n terms of an AP is 4 n - n²  what is the first term (that is S)? what is the sum of first two terms?what is the second term? similarly find the 3rd,the 10th and the nth terms.

(12) Find the sum of first 40 positive integers divisible by 6.

(13) Find the sum of first 15 multiples of 8.

(14) Find the sum of odd numbers between 0 and 50.

(15) A contract on construction job specifies a penalty for delay for completion beyond a certain due date as follows. \$200 for the first day, \$250 for the second day, \$300 for the third day etc., the penalty for each succeeding day being \$50 more than for the preceding day. How much money the contractor has to pay as penalty,if he has delayed the work be 30 days.    Solution

(16) A sum of \$700 is to be used to seven cash prizes to students of a school for their overall academic performance. If each prize is \$20 less than the preceding prize, find the value of each prizes.           Solution

(17) In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in each they are studying ,e.g, a section  of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. There are three sections of each class. How many trees will be planted by the students?     Solution

(18) A spiral is made up of successive semicircles,with centres alternately at A and B starting with center at A of radii 0.5, 1.0 cm, 1.5 cm ,2.0 cm ......... as shown in figure . What is the total length of spiral made up of thirteen consecutive semicircles. (∏ = 22/7)   Solution

After having gone through the stuff given above, we hope that the students would have practiced questions in this worksheet.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6