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

The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term

Find the 20th term from the end of the AP 3, 8, 13……..253

If the pth, qth & rth term of an AP is x, y and z respectively,
show that x(qr) + y(rp) + z(pq) = 0 
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.

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

Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5.

Find the value of x if 2x + 1, x2 + x +1, 3×2 – 3x +3 are consecutive terms of an AP

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.

Prove that am + n + am – n =2am

If the roots of the equation (bc)x2 +(ca) x +(ab) = 0 are equal show that a, b, c are in AP.
Also see:
 HOTS Questions of Mathematics (CIRCLES)
 HOTS Questions of Mathematics (COORDINATE GEOMETRY)
 HOTS Questions of Mathematics ( Heights & Distance)
 HOTS Questions of Mathematics (CONSTRUCTIONS)
 HOTS Questions of Mathematics ( ARITHMETIC PROGRESSIONS)
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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
1.The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term
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
10.If the roots of the equation (bc)x2 +(ca) x +(ab) = 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
26. If (x2 – y2) = 10 and (x + y) = 2, find x and y.
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I want the explanation for the query given below:
In an AP, prove that Am+n+Amn=2Am, where An is the nth term.
find the sum of three digit number which leave remainder 3 when divided by 5?
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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+(ab)/(pq)}
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
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.
the sum of first q terms of an ap is 63q3q2.if its pth term is 60 find p.
The sum of three numbers in AP is 12 and the sum of their cubes is 228. Find the numbers.
What is a.p. And relate its terms explain and formulas and pattern term difference arithmetic progression
If the roots of the equation (bc)x2 +(ca) x +(ab) = 0 are equal show that a, b, c are in AP.
i m unable to solve this and i need help
The 4th term of an arithmetic progression is zero.prove that its 25th term is triple its 11th term
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?
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.
the fourth term of an arithmetic progression is zero.prove that its 25th term is triple its 11th term.