हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Sn = `("a"("r"^"n" - 1))/("r" - 1)`

∴ S5 = `("a"("r"^5 - 1))/("r" - 1)` = 1023, where r = 4

∴ `("a"(4^5 - 1))/(4 - 1)` = 1023

∴ `("a"(1024 - 1))/3` = 1023

∴ a = 3

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Sequences and Series - Exercise 2.2 [पृष्ठ ३१]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 2 Sequences and Series
Exercise 2.2 | Q 2. (ii) | पृष्ठ ३१

संबंधित प्रश्न

Which term of the following sequence: 

`2, 2sqrt2, 4,.... is 128`


Which term of the following sequence:

`sqrt3, 3, 3sqrt3`, .... is 729?


Evaluate `sum_(k=1)^11 (2+3^k )`


Find the value of n so that  `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.


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


If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.


If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.


Find:
the ninth term of the G.P. 1, 4, 16, 64, ...


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


Which term of the G.P. :

\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]


The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.


If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.


Find the sum of the following geometric progression:

1, 3, 9, 27, ... to 8 terms;


Find the sum of the following serie to infinity:

\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]


Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.


Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.


If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.


If a, b, c are in G.P., prove that:

\[a^2 b^2 c^2 \left( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \right) = a^3 + b^3 + c^3\]


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

\[\frac{ab - cd}{b^2 - c^2} = \frac{a + c}{b}\]


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.


If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then P2 is equal to


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 


Let x be the A.M. and yz be two G.M.s between two positive numbers. Then, \[\frac{y^3 + z^3}{xyz}\]  is equal to 


Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.


If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.


The numbers 3, x, and x + 6 form are in G.P. Find 20th term.


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


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:

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


If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term


Find : `sum_("n" = 1)^oo 0.4^"n"`


If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.


Select the correct answer from the given alternative.

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


Answer the following:

For a sequence , if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.


Answer the following:

If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q


The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×