Advertisements
Advertisements
प्रश्न
Find the 4th term from the end of the G.P.
Advertisements
उत्तर
\[\text { Here, first term, } a = \frac{2}{27}\]
\[\text { Common ratio}, r = \frac{a_2}{a_1} = \frac{\frac{2}{9}}{\frac{2}{27}} = 3 \]
\[\text { Last term, } l = 162\]
\[\text { After reversing the given G . P . , we get another G . P . whose first term is l and common ratio is } \frac{1}{r} . \]
\[ \therefore 4th \text { term from the end } = l \left( \frac{1}{r} \right)^{4 - 1} = (162) \left( \frac{1}{3} \right)^3 = 6\]
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
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`.
Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. 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:
(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;
Find the sum of the following geometric series:
`sqrt7, sqrt21, 3sqrt7,...` to n terms
Evaluate the following:
\[\sum^{10}_{n = 2} 4^n\]
Find the sum of the following series:
7 + 77 + 777 + ... to n 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 fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
Find the sum of 2n terms of the series whose every even term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.
Find the sum of the following serie to infinity:
8 + \[4\sqrt{2}\] + 4 + ... ∞
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
If a, b, c, d are in G.P., prove that:
(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.
Find the geometric means of the following pairs of number:
2 and 8
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 second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
For the G.P. if a = `2/3`, t6 = 162, find r.
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
The numbers 3, x, and x + 6 form are in G.P. Find x
For the following G.P.s, find Sn
3, 6, 12, 24, ...
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. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
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.
If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
Answer the following:
Find `sum_("r" = 1)^"n" (2/3)^"r"`
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 in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
