ARITHMETIC SERIES WORKSHEET

(1)  Find the sum of first 75 positive integers.

Solution

(2)  Find the sum of first 125 natural numbers

(3)  Find the sum of 6 + 5 ¼ + 4 ½ + ......... 25 terms

(4)  Find the sum of each arithmetic series described

a = 5, n = 30 and L = 121

(5)  Find the sum of each arithmetic series described

a = 50, n = 25 and d = -4

(6)  Find the sum of first 40 terms of the series

12 - 22 + 32 - 42  + ........

Solution

(7)  How many terms of the AP

9, 17, 25,..........

must be taken to give a sum of 636?

(8)  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.

(9)  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

(10)  Find the sum of all 3 digit natural numbers, which are divisible by 9.   Solution

(11)  Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.       Solution

(12)  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

(13)  Find the sum of all natural numbers between 300 and 500 which are divisible by 11.     Solution

(14)  Find the  sum of all natural numbers between 100  and 200 which are not divisible by 5.        Solution

(15)  Solve 1 + 6 + 11 + 16 + ..........  + x = 148

Solution

(16)  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

(17)  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

(18)  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

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Domain and range of rational functions

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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