Selecting Consecutive Terms in A.P

Q.

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.

Q.

What is the next number in the series $0,6,24,60,120,210,$?

Q. The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$, then what is the length of its smallest side?

Q. If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be

1. 5
2. 7
3. 9
4. 11

Q.

Three number are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.

Q.

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are

1. None of these

2. 3, 7, 11, 15

3. 5, 10, 15, 20

4. 4, 10, 16, 22

Q.

The sum of all natural numbers which are divisible by 3 and less than 100 is

1. 1863

2. 1368

3. 1763

4. 1683

Q.

Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.

Q. Find sum of n terms series :1×2×3+2×3×4+3×4×5+.....

Q. Let $a,b,c,d$ be distinct real numbers such that $a,b$ are roots of $x^2-5cx-6d=0,$ and $c,d$ are roots of $x^2-5ax-6b=0.$ Then $b+d$ is

1. $180$
2. $144$
3. $126$
4. $162$

Q.

The sum of each of two sets of three terms in A.P. is 15. The common difference of the first set is greater than that of the second by 1 and the ratio of the products of the terms in the first set and that of the second set is 7:8 the ratio of the smallest terms in two sets of terms is

1. None

2. $\frac{3}{4}or\frac{11}{12}$

3. $\frac{2}{3}or\frac{1}{2}$

4. $\frac{2}{3}or\frac{3}{4}$

Q.

If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.

Q. The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as $1:120$. Find the angles in radians.

Q. The sum of all distinct roots of the equation $(x^2-11x+29{)}^{(x^2-8x+7)}=1$ is

1. $12$
2. $16$
3. $17$
4. $19$

Q.

In winter, the temperatures at a hill station from Monday to Friday are in A.P. The sum of the temperatures from Monday to Wednesday is $0$, while the sum of the temperatures on Thursday and Friday is $15$. Find the temperatures on each of the weekdays.

Q. Find the missing term in the following series.
$0,4,18,48,?,180$

1. $100$
2. $191$
3. $152$
4. $110$

Q.

The value of p $>$ 0, for which both the equations $x^2+px+64$ = 0 and $x^2-8x+p$ = 0 have real roots is:

1. 8

2. 16

3. 32

4. None

Q. If given $5$ times the fifth term of an $A.P$. is equal to $8$ times its eight term, show that its ${13}^{th}$ term is zero.

Q.

The angles of a quadrilateral are in A.P. whose common difference is ${10}^{\circ }$. Find the angles.

Q. In an $A.P.,$ the first term is $2$ and the sum of the first five terms in one-fourth of the next five terms. Show that ${20}^{th}$ term is $-112.$

Q. The degree measures of the angles in a convex $18$-sided polygon form an increasing arithmetic sequence with integer values. If $x$ is the degree measure of the smallest angle, then the number of divisors of $x$ is
(correct answer + 3, wrong answer 0)

Q. Five numbers are in A.P., whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$, then the greatest number amongst them is

1. $\frac{21}{2}$
2. $16$
3. $7$
4. $27$

Q.

The sum of all natural numbers which are divisible by 3 and less than 100 is

1. 1863

2. 1368

3. 1683

4. 1763

Q.

The sum of each of two sets of three terms in A.P. is 15. The common difference of the first set is greater than that of the second by 1 and the ratio of the products of the terms in the first set and that of the second set is 7:8 the ratio of the smallest terms in two sets of terms is

1. $\frac{3}{4}or\frac{11}{12}$

2. $\frac{2}{3}or\frac{1}{2}$

3. $\frac{2}{3}or\frac{3}{4}$

4. None

Q.

Find the sum of the first n terms of the series: 3 + 7 + 13 + 21 + 31 + …

Q. If n÷n =1 means then 0÷0 is also equals to 1
but y it can't be

Q.

If $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P., prove that:
(i) $\frac{b+c}{a},\frac{c+a}{b},\frac{a+b}{c}$ are in A.P.
(ii) $a(b+c),b(c+a),c(a+b)$ are in A.P.

Q. If the angles of a quadrilateral are in A.P. whose common difference is ${10}^{\circ }$, then the angles of the quadrilateral are

1. , , ,
2. , , ,
3. , , ,
4. , , ,

Q.

If P(A) = 1/3, P(B) = 1/2 and P(A U B) = 2/3, then

1. 1/4

2. 4/3

3. 1/3

4. 1/2

Q. If roots of the equation $x^2-10cx-11d=0$ are a, b and those of $x^2-10ax-11b=0$ are c, d, then the value of a + b + c + d is (a, b, c and d are distinct numbers)