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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from the given alternative. The tenth term of the geometric sequence 14,-12,1,-2, ... is –

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प्रश्न

Select the correct answer from the given alternative.

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –

पर्याय

  • 1024

  • `1/1024`

  • – 128

  • `(-1)/28`

MCQ
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उत्तर

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is – 128

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४०]

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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. (2) | पृष्ठ ४०

संबंधित प्रश्‍न

Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio


The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.


Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn


Find :

the 12th term of the G.P.

\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]


Which term of the G.P. :

\[2, 2\sqrt{2}, 4, . . .\text {  is }128 ?\]


Which term of the G.P.: `sqrt3, 3, 3sqrt3`, ... is 729?


Find three numbers in G.P. whose sum is 38 and their product is 1728.


The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.


The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is \[87\frac{1}{2}\] . Find them.


Find the sum of the following geometric series:

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


The ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.


A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.


Let an be the nth term of the G.P. of positive numbers.

Let \[\sum^{100}_{n = 1} a_{2n} = \alpha \text { and } \sum^{100}_{n = 1} a_{2n - 1} = \beta,\] such that α ≠ β. Prove that the common ratio of the G.P. is α/β.


Find the sum of the following serie to infinity:

8 +  \[4\sqrt{2}\] + 4 + ... ∞


If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.


If a, b, c are in G.P., prove that the following is also in G.P.:

a2 + b2, ab + bc, b2 + c2


If a, b, c, d are in G.P., prove that:

(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.


If (a − b), (b − c), (c − a) are in G.P., then prove that (a + b + c)2 = 3 (ab + bc + ca)


If pth, qth, rth and sth terms of an A.P. be in G.P., then prove that p − q, q − r, r − s are in G.P.


Insert 5 geometric means between 16 and \[\frac{1}{4}\] .


If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.


The fractional value of 2.357 is 


If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is 


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

1, –5, 25, –125 …


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

3, 4, 5, 6, …


Which term of the G.P. 5, 25, 125, 625, … is 510?


For what values of x, the terms `4/3`, x, `4/27` are in G.P.?


The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz


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

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


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

`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`


Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"` 


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 perimeters of all the squares


Select the correct answer from the given alternative.

If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?


Select the correct answer from the given alternative.

If common ratio of the G.P is 5, 5th term is 1875, the first term is -


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 –


Answer the following:

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


If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.


If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is `(q^p/p^q)^(1/(p - q))`


The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is ______.


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