Arithmetic sequence worksheet :
Exercise 2.1
Questions
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Solution
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(1)The first term of an A.P is 6 and the common difference is 5. Find the A.P and its general term
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(2) Find the common difference and 15 th term of an A.P 125 , 120 , 115 , 110 , ……….….
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(3) Which term of the arithmetic sequence is 24 , 23 ¼ ,22 ½ , 21 ¾ , ………. Is 3?
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(4) Find the 12th term of the A.P √2 , 3 √2 , 5 √2 , …………
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(5) Find the 17th term of the A.P 4 , 9 , 14 ,…………
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(6) How many terms are there in the following A.P
(i) -1,-5/6,-2/3,……………10/3
(ii) 7,13,19,……………205
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(7) If 9th term of an A.P is zero, prove that its 29th term is double (twice) the 19th term
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(8)The 10th and 18th terms of an A.P are 41 and 73 respectively. Find the 27th term
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(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,...........
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(10) How many two digit numbers are divisible by 13?
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(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.
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(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?
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(13) The sum of three consecutive terms in an A.P is 6 and their product is -120. Find the three numbers
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(14) Find the three consecutive terms in an A.P whose sum id 18 and the sum of their squares is 140.
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(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.
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(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.
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(17) If a , b , c are in A.P then prove that (a-c)² = 4 (b²-ac)
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(18) If a ,b , c are in A.P then prove that (1/bc),(1/ca),(1/ab) are also in A.P
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(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
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(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
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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