(1) Find the sum of first 75 positive integers.
(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
1^{2} - 2^{2} + 3^{2} - 4^{2} + ........
(7) How many terms of the AP
9, 17, 25,..........
must be taken to give a sum of 636? Solution
(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. Solution
(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 3^{rd} term is 7 and 7^{th} term is 2 more than three times its 3^{rd} 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
(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.
(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.
(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?
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