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Select the correct answer from the given alternative. Sum to infinity of a G.P. 5, -52,54,-58,516,... is –

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प्रश्न

Select the correct answer from the given alternative.

Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is –

पर्याय

  • 5

  • `-1/2`

  • `10/3`

  • `3/10`

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उत्तर

Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is `10/3`

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पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४१]

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बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (7) | पृष्ठ ४१

संबंधित प्रश्‍न

Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).


The sum of first three terms of a G.P. is  `39/10` and their product is 1. Find the common ratio and the terms.


If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that `a^(q - r) b^(r-p) c^(p-q) = 1`.


Insert two numbers between 3 and 81 so that the resulting sequence is G.P.


Show that one of the following progression is a G.P. Also, find the common ratio in case:

4, −2, 1, −1/2, ...


Show that one of the following progression is a G.P. Also, find the common ratio in case:

−2/3, −6, −54, ...


Show that one of the following progression is a G.P. Also, find the common ratio in case:

\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]


Find:

the 10th term of the G.P.

\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]

 


Find the 4th term from the end of the G.P.

\[\frac{2}{27}, \frac{2}{9}, \frac{2}{3}, . . . , 162\]

Which term of the G.P. :

\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, \frac{1}{4\sqrt{2}}, . . . \text { is }\frac{1}{512\sqrt{2}}?\]


If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.


The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.


Find the sum of the following geometric progression:

2, 6, 18, ... to 7 terms;


Find the sum of the following geometric series:

\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]


Find the sum of the following geometric series:

(x +y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... to n terms;


Find the sum of the following geometric series:

\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]


Find the sum of the following geometric series:

x3, x5, x7, ... to n terms


Find the sum of the following geometric series:

`sqrt7, sqrt21, 3sqrt7,...` to n terms


Find the sum of the following series:

7 + 77 + 777 + ... to n terms;


The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.


Find the sum of the following series to infinity:

10 − 9 + 8.1 − 7.29 + ... ∞


If a, b, c are in G.P., prove that:

(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.


If a, b, c are in A.P., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.


If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.


Find the geometric means of the following pairs of number:

2 and 8


If the fifth term of a G.P. is 2, then write the product of its 9 terms.


The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 


Check whether the following sequence is G.P. If so, write tn.

2, 6, 18, 54, …


Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1


For the following G.P.s, find Sn

3, 6, 12, 24, ...


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

p, q, `"q"^2/"p", "q"^3/"p"^2,` ...


If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.


Express the following recurring decimal as a rational number:

`2.bar(4)`


The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares


Select the correct answer from the given alternative.

Which term of the geometric progression 1, 2, 4, 8, ... is 2048


Answer the following:

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


Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r


Answer the following:

If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2   


The sum of the infinite series `1 + 5/6 + 12/6^2 + 22/6^3 + 35/6^4 + 51/6^5 + 70/6^6 + ....` is equal to ______.


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