Advertisements
Advertisements
Question
For a G.P. if S5 = 1023 , r = 4, Find a
Advertisements
Solution
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
APPEARS IN
RELATED QUESTIONS
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is `1/r^n`.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric progression:
4, 2, 1, 1/2 ... to 10 terms.
The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.
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.
The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
Find the rational number whose decimal expansion is `0.4bar23`.
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.
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 are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
Insert 6 geometric means between 27 and \[\frac{1}{81}\] .
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
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.
1, –5, 25, –125 …
For the following G.P.s, find Sn
0.7, 0.07, 0.007, .....
For a G.P. a = 2, r = `-2/3`, find S6
Find : `sum_("r" = 1)^oo (-1/3)^"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.
Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is –
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.
