TAPASYA ACADEMY CBSE CLASS X MATHS ASSIGNMENT

ARITHMETIC PROGRESSION

1) 2, 4 6,3 2k k k are the 3 consecutive terms of an A.P. The value of k is ____________

2) The product of two numbers is 91 and their A.M is 10. The numbers are ____________

3) The sum of all the integers between 50 and 350 which end in 1 is ______________

4) The general term of the A.P 3 , , 5 ,.....x b x b x b is 4x b . Then __________________

5) The sum of first n natural numbers is 105. The value of n is _________________

6) The sum of first n terms of an A.P is 22 3n n . The rth term of the A.P is ______

7) Fourth term in the sequence defined by 1 2 3t t and 1 4 2n nt t n is ________

8) If ,1024, are in A.P. then their A.M. is ________________________

9) The sum to r terms of the series 1 2 3 ......a a a is ________________________

10) 1 2 3, , ,..., na a a a are in AP such that 4 8 12a a a k , the sum of its first 15 terms is

____________________________

11) Two APs have the same common difference. The first term of one of these is 80

and that of the other is 20. The difference between their 2013th terms is ____________

12) In an AP, if the sum of 1606th and 405th terms is 20 then the sum of first 2005

terms is _____________________________________

13) The sums of k terms of two APs are in the ratio 5 2 : 5k k , then the ratio of

their 101st terms is _____________________________

14) Let 1 2 3, , ,......a a a and 1 2 3, , ,......b b b are the arithmetic progressions such that 1 25a ,

1 75b and 100 100 100a b . The sum of the first one hundred terms of the progression

1 1 2 2 3 3, , ,......a b a b a b is _____________________________________

15) The measures of the interior angles of a convex polygon are in A.P. If the smallest

angle is 100 and the largest angle is 140 , then the number of sides of polygon is

____________________________________

16) The number of terms of the A.P 116, , 5,......2

needed to give the sum 25 is

________

17) The three sides of a right triangle have integral lengths which form an A.P. One of

the side could have length [

] A) 22 B) 58 C) 81 D) 91

18) Let x y and the sequences 1 2, , ,x a a y and 1 2, , ,x b b y each are in A.P. Then

2 1

2 1

a ab b

equals to _________________

19) A circle with area 1A is contained in the interior of a large circle with area 1 2A A .

If the radius of the largest circle is 3 and 1 2 1 2, ,A A A A are in A.P, then the radius of

the smaller circle is _________________

20) If the sum of the first 10 terms and the sum of the first 100 terms of a given

arithmetic progression are 100 and 10 respectively. Then the sum of the first 110

terms is _____________________

21) The ratio of kth terms of two APs are in the ratio 2 3 : 3 1k k , then the ratio of

their sums to first 101 terms is ______________________________

22) The sum of the odd positive integers from 1 to n is 10201. The value of n is

____________________________

23) If a, b, c are in AP prove that:

a) 2 2 2, ,a b c b c a c a b b) 1 1 1, ,b c c a a b

c) , ,a b c b c a c a bbc ca ab

d) 1 1 1 1 1 1 1 1 1, ,a b c b c a c a b

are also in AP.

24) If , ,b c a c a b a b ca b c

are in AP, prove that 1 1 1, ,a b c

are also in AP.

25) Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

26) The sum of n terms of two APs are in the ratio 7 1 : 4 27n n . Find the ratio of

their nth terms.

27) Find four numbers in increasing A.P such that their sum and product are

respectively 16 and 105. (1, 3, 5, 7 or 151 1514 151, 4 ,4 , 4 1513 3

)

28) Prove that line segment joining the midpoints of non-parallel sides of a trapezium

is equal to the AM of parallel sides.

29) In an AP, the sum of the first and third term is one more than the fourth term.

When twice the second term is added to fifth term we get two more than the ninth

term. Find the progression.

30) In an AP, the fourth term is 8 times the first term. The sum of the second term

and fourth term is 4 less than the 6th term. Find the progression.

31) For an AP, the sum of the first, second and the fourth terms is zero. The ninth

term is four times the fourth. Find the progression.

32) The first term of an AP is 10 and the common difference is 2 . How many terms

must be taken to get a sum 24. Explain the double answer.

33) The sum of 3 numbers in AP is 27 and their product is 585. Find them.

34) The sum of five numbers in AP is 5 and the sum of their cubes is 385. Find them.

35) Divide 16 into four parts which are in AP and whose product is 105. Find them.

36) If 2 2 2, ,a b c are in AP prove that 1 1 1, ,b c c a a b

are also in AP.

37) If 2 2 2, ,b c c a a b are in AP prove that 1 1 1, ,b c c a a b

are also in AP.

38) If the mth, rth, nth terms of an AP are respectively x, y, z, evaluate

a) x r n y n m z m r b) x y zr n n m m rm r n

39) mth term of an AP is n and nth term is m. Show that (m+n)th term is zero and rth

term is m n r .

40) If m times the mth term and n times the nth term of an AP are equal, show that

(m+n)th term is zero.

41) If the sum of first 2n terms of the AP 2, 5, 8, is equal to the sum of first n terms

of the AP 57, 59, 61, , find n.

42) A person agrees to buy a used scooter worth Rs. 12000. He pays Rs. 6000 and

agrees to pay the balance in monthly installments of Rs. 500 plus 18% interest per

annum on the unpaid amount. What will the scooter cost him at the end?

43) The sum of 6 terms which form an A.P. is 345. The difference between the first

and last terms is 55. Find the terms.

ANSWERS

1) 3 2) 7, 13 3) 5880 4) 74

n

5) 15 6) 6 1r 7) 11 8) 1024

9) 21 22 ar r r 10) 5k 11) 60 12) 20100

13) 1003:206 14) 10000 15) 6 16) 5 or 20

17) C 18) 1 19) 3 20) 110

21) 99:154 22) 201 25) 3050 26) 14 6 : 8 23n n

27) 1, 3, 5, 7 or 151 1514 151, 4 ,4 , 4 1513 3

29) There are infinitely many such progressions in which 1d a

30) 3, 10, 17,

31) There are infinitely many such progressions in which 3 4 0a d

32) 3, 8

33) 13, 9, 5

34) 3, 1,1,3,5

35) 1, 3, 5, 7

38) a) 0 b) 0

41) 11

42) Rs. 12585

43) 30, 41, 52, 63, 74, 85