mathematics extra questions class x sa 2 pc - 17 maths extra qns (a.p.,) sa2

7/25/2019 MATHEMATICS EXTRA QUESTIONS CLASS X SA 2 PC - 17 Maths Extra Qns (a.P.,) SA2

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MATHEMATICS EXTRA QUESTIONS CLASS X SA 2

ARITHMETIC PROGRESSION

1)Find t 10of the A.P., 1, 8,15,(t n, a n are the same.)

2)Find the 21st

term of the A.P., 100, 97,94.

3)If in an A.P., t 11 = 33 and t 20 = 63, find a , d.

4)Find the sum of the first 100 multiples of 3.

5)Find the sum of all two digit numbers which are divisible by 4.

6) Find the sum of all 3 digit numbers which leaves remainder 1 when

divided by 6.

7)Find sum of all 3 digit numbers which are all divisible by 2 and 3.

8)Find the sum of all 2 digit numbers which are divisible by 3 or 4.

9)Find S 100of 1,4,7,.

10)If S n= 4 n 2+ 5n, show that the sequence forms an A.P.

11)If the ratio between sum of first n terms of two A.Ps is

(4n+5) :(5n+1), find the ratio between the 11th

terms.

12)Find the sum of the last 10 terms of the A.P., 1,3,5,..217.

13)In the A.P., a, a+d, a+2d, ,l, show that the number of terms

n = ((la ) / d )+ 1 .

14)In the A.P., a, a+d,a+2d.. , show that S n= (n/2)( 2a + ( n-1)d) or

S n= (n/2)(a + l ) if the last term is known as l. (rsr)


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15)If a boy keeps tiny marbles in a chess board in the following

manner: 1 marble in the first square, 6 marbles in the second

square,11 in the third square and so on. Find the number of marbles

kept by the boy in the last square and also the total number ofmarbles in the whole chess board.(Recall that there are 64 squares in

a chess board.).

16)Name the A.Ps in the following cases with

reasons:(i)2,5,8,.(ii)4,1,-2,..(iii)5,5,5,..

17)In the general A.P., a, a+d,(i) if the same constant k is being

added to each of the terms, show that the new sequence is also an

A.P.,(ii) if the same constant k is being subtracted from each of the

terms, show that the new sequence is also an A.P.,(iii)if the same non-

zero constant k is being multiplied, show that the new sequence is

also an A.P.,(iv)if each term is divided by the same non-zero constant

k, show that the new sequence is also an A.P.,

18)In a sequence, S n= a n2

+ b n ,where a , b c are constants, check ifthe sequence forms an A.P., or not. If so, find the first term and

common difference.

19)A man starts his salary with Rs.10,000/- per month. He gets an

annual increment of Rs.2000/-at the beginning of every year. Find his

monthly salary at the beginning of his 21st

year in the organization

and the total amount of salary earned by him till the 20th

year.

20)In a three digit number, digits are in A.P., Sum of the digits is 6. If

we add 198 to the number the digits get reversed. Find the number.

(rsr)


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21)Sum of three numbers in A.P., is 12 and sum of their squares is 66.

Find the numbers.

22)Sum of five numbers in A.P., is 15 and sum of their squares is 55.

Find the numbers.

23)If a,b,c are in A.P., show that 2 b = ( a + c).

24)Find the number of terms to be added in 1,3,5 to get the sum as

10201.

25)Find the number of terms to be added from 1,4,7, to get the sum

as 3876.26)Is 401 a term of the sequence 1,5,9,13,.?

27)Is 303 a term of the sequence 2,5,8,? Justify your answer.

28)Which term of the A.P., 100,97,94,. is the first negative term?

Also find the term.

29)Prove using concept of A.P., the sum of first n natural numbers is

n ( n+1)/2.

30)Find the sum of first 11 terms of an A.P.,if the middle term is 40

assuming that there are 11 terms in the A.P.,

31)If S ndenotes the sum of the first n terms in an A.P.,, show that

S 15 = 3 ( S 10S 5).

32)A man starts saving money in the month of March as follows:

Rs.2/- in the first day, Rs.7/- in the second day,Rs.12/- in the 3rd

day

and so on. Find the amount saved by him in the last day of the month

and also find the total amount saved by him in the whole month. (rsr)


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33)The sum of first ten terms of an A.P., is 100 and that of twenty

terms of 400. Find a,d,S 30. 34)Find the sum of last ten terms of

1,3,5201.

35)In an A.P., 10 thterm is 28 and 20 th term is 58. Find the sum of first

51 terms.

36)The sum of first ten terms of an A.P., is 145 and the sum of the

next ten terms is 445. Find a, d, S 15.

37)In an A.P.,t 3 or a 3= 10 and t 9 or a 9= 28,find a ,d and S 100.

38)In an A.P., first term is 1 and last term is 41 and their sum is 231.

Find the number of terms and common difference.

39)Find the number of terms in 2,6,10,...,402.

40)Using the concept of A.P., prove that the sum of first n odd natural

numbers is n2

. 41)Find 1+6+11+..upto 101 terms

42)The sum of five numbers in A.P., is 25 and sum of their squares is165. Find the numbers.

43)The sum of four numbers in A.P., is 26 and sum of their squares is

214. Find the numbers.

44)Find the number of terms to be added in 20+19+18+ to get the

sum as 210. Write the reason for having double answer.

45)How many terms of 30+28+26+. is to be added to get the sum as

240? Write the reason for double answer.

BEST WISHES R.SANKARARAMAN


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mathematics extra questions class x sa 2 pc - 17 maths extra qns (a.p.,) sa2

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