Arithmetic sequence worksheet :
Here we are going to some practice question. You can find solution for each question with detailed explanation.
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:
Sets and Functions
Exercise 1.2 |
Exercise 1.4 |
Sequence and Series
Algebra
MATRIX
Exercise 4.2 |
Exercise 4.3 |
Coordinate Geometry
Exercise 5.3 | |||
Geometry
Trigonometry
Mensuration
Statistics
Probability
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