Comparing Sn of Two Arithmetic Sequences

Q.

If the sum of the $10$ terms of an A.P. is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is:

1. $1:2$

2. $2:1$

3. $2:3$

4. $3:2$

Q.

The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is

1. 15 or -9

2. -15 or 9

3. -15 or -9

4. 15 or 9

Q.

Three consecutive integers add up to $51$. What are these integers?

Q. The sum of first ten terms of an A.P. is four times the sum of its first five terms, then ratio of the first term and common difference is

1. 1 : 3
2. 1 : 2
3. 3 : 4
4. 1 : 4

Q.

The ratio of the sums of m and n terms of an A.P. is $m^2$ : $n^2$. Show that the ratio of the $m^{th}$ and $n^{th}$ term is $(2m–1):(2n–1)$. [4 MARKS]

Q.

Find the sum of first $n$ natural numbers.

1. $\frac{n(2n+1)}{2}$

2. $\frac{2n+1}{2}$

3. $\frac{n(n+1)}{2}$

4. $\frac{n(2n-1)}{2}$

Q. If the sum of first 10 natural numbers is $S_1$ and that of first 10 whole numbers is $S_2.$ Then $S_1-S_2$ is

1. 20
2. 10
3. 40
4. 30

Q. If any one term of an arithmetic progression along with the position of the term in the A.P. and the common difference are known, then which of the following can be found out.

1. The first term.
2. All of the above.
3. The term before the known term.
4. The term after the known term.

Q.

The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is

1. 15 or -9

2. -15 or 9

3. -15 or -9

4. 15 or 9

Q. The nth term of an Arithmetic geometric progression is given by $[a+(n-1\left)d\right]b{r}^{n-1}$

1. False
2. True

Q. The nth term of an Arithmetic geometric progression is given by $[a+(n-1\left)d\right]b{r}^{n-1}$

1. True
2. False

Q. The nth term of an Arithmetic geometric progression is given by $[a+(n-1\left)d\right]b{r}^{n-1}$

1. True
2. False

Q. The ratio of the sums of m and n terms of an A.P. is $m^2$ : $n^2$. Show that the ratio of the $m^{th}$ and $n^{th}$ term is $(2m–1):(2n–1)$.

Q. The ratio of the sums of m and n terms of an A.P. is $m^2$ : $n^2$. Show that the ratio of the $m^{th}$ and $n^{th}$ term is $(2m–1):(2n–1)$.