Sequences and Series (p-1) - Maharashtra Board STD 11 Commerce / Arts Maths (commerce) Questions

Determine whether the sum to infinity of the following G.P'.s exist. If exists, find it.
(i) $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots$
(ii) $2, \frac{4}{3}, \frac{8}{9}, \frac{16}{27}, \ldots$
(iii) $-3,1, \frac{-1}{3}, \frac{1}{9}, \ldots$
(iv) $\frac{1}{5}, \frac{-2}{5}, \frac{4}{5}, \frac{-8}{5}, \frac{16}{5}, \ldots$

View full solution →

Q 12Solve the Following Question.(3 Marks)3 Marks

Find $\left(50^2-49^2\right)+\left(48^2-47^2\right)+\left(46^2-45^2\right)+\ldots \ldots+\left(2^2-1^2\right)$

View full solution →

Q 13Solve the Following Question.(3 Marks)3 Marks

Find $\sum_{r=1}^n \frac{1^2+2^2+3^2+\ldots+r^2}{2 r+1}$

View full solution →

Q 14Solve the Following Question.(3 Marks)3 Marks

For a sequence, $S_n=4\left(7^n-1\right)$, verify whether the sequence is a G.P.

View full solution →

Q 15Solve the Following Question.(3 Marks)3 Marks

In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term.

View full solution →

Q 16Solve the Following Question.(3 Marks)3 Marks

Find $\left(70^2-69^2\right)+\left(68^2-67^2\right)+\left(66^2-65^2\right)+\ldots \ldots . .+\left(2^2-1^2\right)$

View full solution →

Q 17Solve the Following Question.(4 Marks)4 Marks

Find five numbers in G.P. such that their product is 243 and the sum of the second and fourth numbers is 10.

View full solution →

Q 18Solve the Following Question.(4 Marks)4 Marks

Find 4 numbers in G. P. such that the sum of the middle 2 numbers is $\frac{10}{3}$ and their product is 1.

View full solution →

Q 19Solve the Following Question.(4 Marks)4 Marks

Find three numbers in G.P., such that their sum is 35 and their product is 1000.

View full solution →

Q 20Solve the Following Question.(4 Marks)4 Marks

If $\mathrm{S}_1, \mathrm{~S}_2$, and $\mathrm{S}_3$ are the sums of first $\mathrm{n}$ natural numbers, their squares, and their cubes respectively, then show that:
$
9 S_2^2=\mathrm{S}_3\left(1+8 \mathrm{~S}_1\right)
$

View full solution →

Q 21Solve the Following Question.(4 Marks)4 Marks

Find $n$, if $\frac{1 \times 2+2 \times 3+3 \times 4+4 \times 5+\ldots+\text { upto } n \text { terms }}{1+2+3+4+\ldots+\text { upto } n \text { terms }}=\frac{100}{3}$

View full solution →

Q 22Solve the Following Question.(5 Marks)5 Marks

Find two numbers whose A.M. exceeds G.M. bv 7 and their H.M. by $\frac{63}{5}$.

View full solution →

Q 23Solve the Following Question.(5 Marks)5 Marks

Find two numbers whose A.M. exceeds their G.M. by $\frac{1}{2}$ and their H.M. by $\frac{25}{26}$.

View full solution →

Q 24Solve the Following Question.(5 Marks)5 Marks

If $S_n, S_{2 n}, S_{3 n}$ are the sum of $n, 2 n, 3 n$ terms of a G.P. respectively, then verify that $S_n\left(S_{3 n}-\right.$ $\left.S_{2 n}\right)=\left(S_{2 n}-S_n\right)^2$

View full solution →

Q 25Solve the Following Question.(5 Marks)5 Marks

Find three numbers in G. P. such that their sum is 21 and sum of their squares is 189.
Solution:

View full solution →

Sequences and Series (p-1) question types

Sequences and Series (p-1) questions

Generate a Sequences and Series (p-1) paper free

Sequences and Series (p-1) Maths (commerce) - Sequences and Series (p-1)

Sequences and Series (p-1) question types

Sequences and Series (p-1) questions

Generate a Sequences and Series (p-1) paper free