# CBSE Class X HOTS Questions of Mathematics ( ARITHMETIC PROGRESSIONS)

### ARITHMETIC PROGRESSIONS

1. The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term
2. Find the 20th term from the end of the AP 3, 8, 13……..253
3. If the pth, qth & rth term of an AP is x, y and z respectively,
show that x(q-r) + y(r-p) + z(p-q) = 0
4. Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6.
5. A man arranges to pay a debt of Rs.3600 in 40 monthly installments which are in a AP. When 30 installments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment
6. Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5.
7. Find the value of x if 2x + 1, x2 + x +1, 3×2 – 3x +3 are consecutive terms of an AP
8. Raghav buys a shop for Rs.1,20,000.He pays half the balance of the amount in cash and agrees to pay the balance in 12 annual installments of Rs.5000 each. If the rate of interest is 12% and he pays with the installment the interest due for the unpaid amount. Find the total cost of the shop.
9. Prove that am + n + am – n =2am
10. If the roots of the equation (b-c)x2 +(c-a) x +(a-b) = 0 are equal show that a, b, c are in AP.

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lola kumar on 05 Mar 2011
• cn u plz urgently mail me d imp ques of cce Std X maths
sa-2 paper….my final exams r goin on….maths is on 17th…. plz mail it 2 me fast.

anshul sogani on 15 Mar 2011
• if the sum of p terms of an A.P. is equal to the sum of q terms then show that the sum of its p+q terms is zero

namrata patil on 09 Apr 2011
• 1.The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term

shikha on 09 Jun 2011
• 8.Raghav buys a shop for Rs.1,20,000.He pays half the balance of the amount in cash and agrees to pay the balance in 12 annual installments of Rs.5000 each. If the rate of interest is 12% and he pays with the installment the interest due for the unpaid amount. Find the total cost of the shop

shikha on 09 Jun 2011
• 10.If the roots of the equation (b-c)x2 +(c-a) x +(a-b) = 0 are equal show that a, b, c are in AP
5.A man arranges to pay a debt of Rs.3600 in 40 monthly installments which are in a AP. When 30 installments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment

shikha on 09 Jun 2011
• 26. If (x2 – y2) = 10 and (x + y) = 2, find x and y.
________________________________________

shikha on 09 Jun 2011
• I want the explanation for the query given below:
In an AP, prove that Am+n+Am-n=2Am, where An is the nth term.

Chithra Chandran on 30 Nov 2011
• find the sum of three digit number which leave remainder 3 when divided by 5?

subhi jain on 10 Dec 2011
• chut main land dalne se kya hota h …………….plz tll in trms of mathematics…..

playboy on 19 Jun 2012
• wat is condom how doesit work
muth nikal jaye raat main to kya hota hai……..

dd on 19 Jun 2012
• if in an arithematic progration pth term is a and qth term is b prove that sum of (p+q)th term is p+q/2{a+b+(a-b)/(p-q)}

ram on 07 Jul 2012
• the sum of two nos A n B is 6 times the geometric mean.show that A/B is 2+root 3/2 -root 3

van on 25 Jul 2012
• a circle has a chord AB of length 5cm extended from A outside the circle to point P. A tangent PT is drawn to circle of xcm. find x.

indu negi on 27 Feb 2013
• the sum of first q terms of an ap is 63q-3q2.if its pth term is -60 find p.

albert on 04 Mar 2013
• The sum of three numbers in AP is 12 and the sum of their cubes is 228. Find the numbers.

Shyamal Dhar on 08 Mar 2013
• What is a.p. And relate its terms explain and formulas and pattern term difference arithmetic progression

ubbaid nabi ganie on 16 Mar 2013
• If the roots of the equation (b-c)x2 +(c-a) x +(a-b) = 0 are equal show that a, b, c are in AP.
i m unable to solve this and i need help

Osheen on 26 Mar 2013
• The 4th term of an arithmetic progression is zero.prove that its 25th term is triple its 11th term

azeema on 29 Oct 2013
• A school decided to disburse Rs.4,000 as award to their students for punctuality. The most punctual student was to be awarded Rs.1200 and the next prizes were to be Rs. 200 less than the previus one .
i) Find the number of students who received the award
ii) What value is highlighted in this context?

Sushantdimri on 27 Nov 2013
• on the independence day in a group of children each child gives one gift to the other. if total numbers of gifts are 90 then find the number of children in the group.

hemlata on 01 Mar 2014
• the fourth term of an arithmetic progression is zero.prove that its 25th term is triple its 11th term.

sajal dutta on 08 May 2014