Arithmetic sequence worksheet : Exercise 2.1

Arithmetic sequence worksheet :
Exercise 2.1


Questions
Solution
(1)The first term of an A.P is 6 and the common difference is 5. Find the A.P and its general term
(2) Find the common difference and 15 th term of an A.P 125 , 120 , 115 , 110 , ……….….
(3) Which term of the arithmetic sequence is 24  , 23 ¼ ,22 ½ , 21 ¾ , ………. Is 3?
(4) Find the 12th term of the A.P √2 , 3 √2 , 5 √2 , …………
(5)  Find the 17th term of the A.P 4 , 9 , 14 ,…………
(6) How many terms are there in the following A.P
(i) -1,-5/6,-2/3,……………10/3
(ii) 7,13,19,……………205
(7) If 9th term of an A.P is zero, prove that its 29th term is double (twice) the 19th term
(8)The 10th and 18th terms of an A.P are 41 and 73 respectively. Find the 27th term
(9) Find n so that nth terms of the following two A.P's are the same.
1,7,13,19,.............. and 100,95,90,...........
(10) How many two digit numbers are divisible by 13?
(11) A TV manufacturer has produced 1000 TVs in the seventh year and 1450 TVs in the tenth year.Assuming that the production increases uniformly by a fixed number every year, find the number of TVs produced in the first and in the 15th year.
(12) A man has saved $640 during the first month,$720 in the second month and $800 in the third month. If he continues his savings in this sequence,what will be his savings in the 25th month?
(13) The sum of three consecutive terms in an A.P is 6 and their product is -120. Find the three numbers
(14) Find the three consecutive terms in an A.P whose sum id 18 and the sum of their squares is 140.
(15) If m times the m th term of an A.P is equal to n times the n th term, then show that the (m+n) th term of the A.P is zero.
(16) A person has deposited $25000 in an investment which yield 14% simple interest annually. Do these amounts (principal + interest) form an A.P? If so, determine the amount of investment after 20 years.
(17) If a , b , c are in A.P then prove that (a-c)² = 4 (b²-ac)
(18) If a ,b , c are in A.P then prove that (1/bc),(1/ca),(1/ab) are also in A.P
(19) If a²,b²,c² are in A.P then show that 1/(b+c),1/(c+a),1/(a+b) are also in A.P
(20) If a^x = b^y = c^z, x ≠ 0 , y ≠ 0 , z ≠ 0 and b² = ac then show that 1/x,1/y and 1/z are in A.P
Answers:
1. 6 , 11 , 16 , …………..
2. -225
3. n =29
4. 23 √2
5. 84
6. (i)  n = 27   (ii) n = 34
7. Proved
8. a = 5 d = 4   t27 = 109
9. n = 11
10.    n = 7
11.    2200
12.    2560
13.    -6 , 2 , 10 or 10,2,-6
14.    2,6,10 or 10,6,2
15.    hence proved

16.    95000

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