Arithmetic Progression

Q.

The number of proper subsets of the set {1, 2, 3} is ___.

Q.

Solve ax²-9(a+b)x+(2a²+5ab+2b²)=0

Q.

The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

Q.

If $pth,qth$ and $rth$ term of an $AP$ are $a,b,c$ respectively, then show that

$(a-b)r+(b-c)p+(c-a)q=0$

Q.

What is the general term of a sequence?

Q.

The digits of a positive integer , having three digits are in AP and their sum is 15 .The number obtaining by reversing the digit is 594 less than the original number .find the number

Q.

A diver descends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and descends another 18 feet. At this point, what is his depth in water?

1. -17

2. -21

3. -13

4. -26

Q.

If the $n^{th}$ term of an arithmetic progression is$(5n-2)$.

Find its first term, common difference and ${19}^{th}$ term.

Q.

Find the ${11}^{th}$ term from the last term (towards the first term) of the AP : $10,7,4,...,–62.$

1. $-24$

2. $-16$

3. $-32$

4. $-28$

Q. The number of terms between 1 to 1000 divisible by 7 are ___.

1. 142
2. 143
3. 144
4. 141

Q.

The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.

Q.

Find the tenth term of the AP: $2,7,12...$.

Q.

The sum of $4$ consecutive numbers in an AP is $32$ and the ratio of the product of the first and the last term to the product of two middle terms is $7:15.$ find the number.

Q. The angles of triangle are in A.P. The greatest angle is twice the least. Find the angles of triangle.

Q.

Divide $56$ into $4$ parts which are in AP such that the ratio of products of extremes to the products of means is $5:6.$

Q.

The sum of the first $7$ terms of an AP is $63$ and the sum of it's next $7$ terms is $161$. Find the ${28}^{th}$ term of this AP.

Q.

Find the value of the middle term of the following AP $-6,-2,2,.....,58$

Q.

In an AP of 50 terms the sum of the first 10 terms is 210 and the sum of the last 15 terms is 2565. find the AP.

Q. If $\frac{5+9+13+...tonterms}{7+9+11+...to(n+1)terms}=\frac{17}{16},$then n =

(a) 8

(b) 7

(c) 10

(d) 11

Q.

The sum of three numbers in A.P. is 15 and the sum of the squares of the extreme terms is 58. Find the numbers.

Q.

Determine k so that (3k -2), (4k-6) and (k +2) are three consecutive terms of an AP.

Q.

$4^{th}$ term of an AP is equal to 3 times the first term and $7^{th}$ term exceeds twice the 3rd term by $1.$ Find the first term and the common difference.

Q. If triangle ABC is right angled at C, then find the value of Cos(A+B).

Q. Divide 32 into four parts which are the four terms of an AP such that the product of the first and the fourth term is to the product of the second and the third term is 7 : 15. [CBSE 2014]

Q. Which term of the A.P 121, 117, 113, ..., is its first negative term?

Q.

The sum of a number and its reciprocals is. What are the numbers?

Q. Question 4
Two AP’s have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their ${10}^{th}$ terms is the same as the difference between their ${21}^{st}$ terms, which is the same as the difference between any two corresponding terms?Why?

Q.

Find three numbers in AP whose sum is 15 and product is 80.

Q.

A man saves $Rs200$ in each of the first three months of his service. In each of the subsequent months, his saving increases by $Rs40$ more than the saving of immediately previous month. His total saving from the start of service will be $Rs11040$ after

1. $19$ months

2. $20$ months

3. $21$months

4. $18$months

Q. For what value of k the terms k+1, 3k and 4k+2 are in arithmetic progression.