HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

For the following G.P.s, find S_n

0.7, 0.07, 0.007, .....

For the following G.P.s, find S_n.

`sqrt(5)`, −5, `5sqrt(5)`, −25, ...

For a G.P. a = 2, r = `-2/3`, find S₆

For a G.P. if S₅ = 1023 , r = 4, Find a

For a G.P. if a = 2, r = 3, S_n = 242 find n

For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r

For a G.P. If t₃ = 20 , t₆ = 160 , find S₇

For a G.P. If t₄ = 16, t₉ = 512, find S₁₀

Find the sum to n terms of the sequence.

0.5, 0.05, 0.005, ...

Find the sum to n terms of the sequence.

0.2, 0.02, 0.002, ...

For a sequence, if S_n = 2(3ⁿ –1), find the n^th term, hence show that the sequence is a G.P.

If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P² 

If S_n, S_2n, S_3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that S_n (S_3n – S_2n) = (S_2n – S_n)².

Find: `sum_("r" = 1)^10(3 xx 2^"r")`

Find: `sum_("r" = 1)^10 5 xx 3^"r"`

The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)⁵ = 1.28, (1.05)⁶ = 1.34]

If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)⁵ = 1.47]

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/2, 1/4, 1/8, 1/16,...`

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`2, 4/3, 8/9, 16/27, ...`

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`-3, 1, (-1)/3, 1/9, ...`