Progressions

Q. How many natural number sets of the form $S_n=\{n-4,n-3,n-2,n-1,n,n+1,n+2,n+3,n+4\}$ (n is a natural number $\le$100) and the set does not contain 10 or any integral multiple of 10?

1. 8

2. 9

3. 10

4. 15

Q. If a, b, c (not equal) are in H.P and n > 1, then $a^n+c^n$ is:

1. Less than $2b^n$
2. Less than or equals to $2b^n$
3. More than $2b^n$
4. More than or equals to $2b^n$

Q. What is the maximum sum of the terms in the arithmetic progression 25, 24, 23, 22.......?

1. 325
2. 345
3. 350
4. 332.5

Q. The first and the third terms of an arithmetic progression are equal, respectively, to the first and the third term of a geometric progression and the second term of the arithmetic progression exceeds the second term of the geometric progression by 0.25. Calculate the sum of the first five terms of the arithmetic progression if its first term is equal to 2.

1. 1.5
2. 3.25
3. 2.25 or 25
4. 2.5

Q. Find the sum of the three numbers in G.P whose product is 216 and the sum of the products of them taken in pairs is 126:

1. 28
2. 21
3. None of these
4. $\frac{35}{4}$

Q. If the first two terms of a HP are $\frac{2}{5}$ and $\frac{12}{13}$, respectively, which of the following terms is the largest term?

1. 4th term
2. 5th term
3. 6th term
4. 2nd term

Q. A geometric progression consists of 500 terms. Sum of the terms occupying the odd places when counting from the left is $P_1$ and the corresponding sum of the terms occupying the even places is $P_2$. Find the common ratio.

1. $P_2+\frac{P_1}{P_1}$
2. $P_2+\frac{P_1}{P_2}$
3. $\frac{P_2}{P_1}$
4. $\frac{P_1}{P_2}$

Q. Let $a_1,a_2,\cdots ,a_{10}$ be in A.P. and $h_1,h_2,\cdots ,h_{10}$ be in H.P. If $a_1=h_1=2$ and $a_{10}=h_{10}=3$, then $a_4{h}_7$ is:

1. 5
2. 6
3. 2
4. 3

Q. If x > 1, y > 1, z > 1 are in G.P, then $\frac{1}{1+logx},\frac{1}{1+logy},\frac{1}{1+logz}$ are in

1. A.P
2. H.P
3. G.P
4. None of these

Q. Product of the fourth term and the fifth term of an arithmetic progression is 456. Division of the ninth term by the fourth term of the progression gives Quotient as 11 and the remainder as 10. Find the first term of the progression.

1. - 52
2. - 42
3. - 56
4. - 66