REVISED CMA

16/8/21

1) If the 3rd and 6th terms of an AP are 7 and 13 respectively, find the first term and the common difference.                              3 and 2

2) find the sum of all natural numbers between 100 and 1000 which are multiple of 5.      98450

3) how many terms of the AP -6, -11/2, -5,.... are needed to give the sum -25 ?                            5 or 20.

4) Determine the sum of the first 35 terms of an AP if a₂ = 2 and a₇ = 22.                        2310

5) If the first term of an AP is 2 and the sum of first five terms is equal to one fourth of the sum of the next five terms, show that the 20th term is --112

6) Insert 3 arithmetic mean between 2 and 10.                  4,6,8

7) The sum of three decreasing numbers in AP is 27. If -1, -1, 3 are added to them respectively, the resulting series is in GP. The numbers are 

A) 5,8,13 B)15,9,3 C)13,9,5 D) 17,9,1

8) The sum of all odd numbers between 1 and 100 which are divisible by 3, is..

A) 83667 B) 90000 C) 83660 D) n 

9) If 7th and 13th terms of an AP be 34 and 64 respectively, then its 18th term is.

A) 87   B) 88   C) 89   D) 90 

10) If the sum of p terms of an AP is q and the sum of q terms is q, then the sum of the p + q terms will be..

A) 0    B) p-q   C) p+q   D) -(p-q)

11) If the sum of n terms of AP be n² - n and its common difference is 6, then its first term is..

A) 2    B) 3      C) 1     D) 4 

12) Sum of all two digit numbers which when divided by 4 yield Unity as reminder is..

A) 1200   B)1210.  C)1250.  D) n

13) In n AM's introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3:1, then the value of n is..

A) 6      B) 8      C) 4     D) n 

14) The 1st and last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be.

A) 5     B) 6      C) 7         D) 8 

15) Find the sum of all odd integers from 1 to 1001.                      251001

16) If the ratio between the sums of n terms of two AP is (7n+1):(4n+27) find the ratio of their 11th term.   148: 111

17) If the sum of m terms of an AP be n and the sum of n terms be m, show that the sum of m+n terms is -(m+n).

18) If the sum of n terms of an AP is (pn+ qn²), where p and q are constants, find the common difference.                                   2q

19) In an AP, the first term is 2 and the sum of first five terms is one-fourth of the sum of next terms. Show that the 20th term is - 112 and the sum of first 20 term is -1100.

21) If the sum of n terms of an AP is given by (3n²+ 4n), find its rth term.                                        6r +1

22) The digits of a three-digit numbers are in AP and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.                                    852

23) Between 1 and 31, m numbers have been inserted in such a way that the ratio of 7th and (m-1)th numbers is 5:9. Find the value of m.                                 14

24) In the arithmetic progression whose common difference is non zero, the sum of the first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms the next to 2n terms is 

A) 1/5. B) 2/3  C) 3/4 D) none

25) If four numbers in AP are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are:

A) 5,10,15,20     B) 4,10,16,22

C) 3,7,11,15       D) none

26) The first and the last term of an AP are a and l respectively. if S is the sum of all the terms of the AP. and the common difference is given by (l²-a²)/{k -(l+a)}, then k is

A) S   B) 2S      C) 3S    D) none

27) If the sum of the first n even natural number is equal to K times the sum of the first n odd natural numbers, then k is..

A) 1/n B) (n-1)/n  C)(n+1)/2n D)(n+1)/n  

28) If the first, second and last term of an AP are a,b and 2a respectively, then its sum is 

A) ab/{2(b-a)}       B) ab/(b-a)

C) 3ab/{2(b-a)}     D) none

29) If x is the sum of an arithmetic progression of n odd number of terms and y the sum of the terms of the series in odd places, then x/y is

A) 2n/(n+1)               B) n/(n+1)

C) (n+1)/2n               D) (n+1)/n 

30) If the first term of an AP is 2 and common difference is 4, then the sum of its 40 terms is

A) 3200 B) 1600 C) 200 D) 2800

31) The number of terms of the AP 3, 7, 11, 15, ... to be so that the sum is 406 is...

A) 5 B) 10 C) 12  D) 14   E) 20

32) If a(1/b+ 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP , then

A) a, b, c are in AP

B) 1/a, 1/b, 1/c are in AP

C) a, b, c are in HP

D) 1/a, 1/b, 1/c are in GP. 

33) If the sum of the three numbers in AP be 18 then what is the middle term ?                                       6

34) The fifth term and the 11th term of an AP are 41 and 20 respectively. Find the first term. What will be the sum of first 11 terms of the AP. ?          425/2

35) The n-th term of an AP is p. Show that sum of first (2n-1) terms is (2n-1)p.

36) The middle term, of an AP having 11th term is 12. Find the sum of the 11 terms of that progression.                               132

37) There are n arithmetic means between 4 and 31. If the second mean : last mean=5: 14 then find the value of n.                         8

38) If the sum of the first P terms of an AP be equal to the sum of the first Q terms then show that the sum of the first P +Q terms is zero.

) Find the sum upto n terms of the series 1²- 2²+ 3²- 4²+ 5²- 6²+.. ..          -n/2 (n+1) (n= 2r)

39) if the sum of p terms of an AP is to the sum of q terms as p²:q², show that (pth term)/(qth term)= (2p-1)/(2q-1).

40) The first term of an AP is a, the second term is b and the last term is c. Show that the sum is {(a+c)(b+c-2a)}/{2(b-a)}.

41) The sides of a right angled triangle are in AP. if the smallest side is 5cm then find the largest side.                                  25/3

42) find the sum of natural numbers from 1 to 200 excluding those divisible by 5.                           16000 

43) Show that the sum of all odd numbers between 2 and 1000 which are divisible by 3 is 83667 and of those not divisible by 3 is 166332.

44) Find the 14 A. M which can be inserted between 5 and 8 and show that their sum is 14 times the Arithmetic mean between 5 and 8.

45) Divide 25/2 into five parts in AP, such that the first and the last parts are in the ratio 2: 3.     2,9/4,5/2, 11/3, 3.

46) For what value of m, the sequence 2(4m+7), 6m + 1/2, 12m-7 forms an AP.               -3/4 

47) Find the 20th term of the AP 80, 75, 70,... Calculate the number of terms required to make the sum equal to zero.                         35 

48) Prove that if unity is added to the sum of any number of terms of the AP 3, 5,7,9...the resulting sum is a perfect square.

49) The sum of n terms of the series 25, 22, 19, 16,.. is 116. Find the number of terms and the last term. The given series is AP.  18405

50) Find the sum of all natural numbers from 100 to 300:

a) which is divisible by 4.       10200

b) excluding those which are divisible by 4.                        30000

c) which are exactly divisible by 5. 

d) which are exactly divisible by 4 and 5.               8200, 2200

e) which are exactly divisible by 4 or 5.                                        16200