मराठी

The third term of G.P. is 4. The product of its first 5 terms is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

The third term of G.P. is 4. The product of its first 5 terms is ______.

पर्याय

  • 4

  • 4

  • 4

  • None of these

MCQ
रिकाम्या जागा भरा

उत्तर

The third term of G.P. is 4. The product of its first 5 terms is 45.

Explanation:

Given that T3 = 4

⇒ ar3–1 = 4

⇒ ar2 = 4

Product of first 5 terms = a · ar · ar2 · ar3 · ar4

= a5r10

= (ar2)5

= (4)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Sequences and Series - Exercise [पृष्ठ १६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 9 Sequences and Series
Exercise | Q 18 | पृष्ठ १६३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .


If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.


The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.


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


Find :

the 8th term of the G.P. 0.3, 0.06, 0.012, ...


Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?


Which term of the G.P. :

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


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 \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.

 

Find the sum of the following series:

0.5 + 0.55 + 0.555 + ... to n terms.


If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.


Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.


Find the rational numbers having the following decimal expansion: 

\[0 . 6\overline8\]


Three numbers are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.


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.


If A1, A2 be two AM's and G1G2 be two GM's between and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]


If the first term of a G.P. a1a2a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is


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


Given that x > 0, the sum \[\sum^\infty_{n = 1} \left( \frac{x}{x + 1} \right)^{n - 1}\] equals 


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 


For the G.P. if a = `2/3`, t6 = 162, find r.


The numbers x − 6, 2x and x2 are in G.P. Find 1st term


The numbers x − 6, 2x and x2 are in G.P. Find nth term


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


If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P


Express the following recurring decimal as a rational number:

`2.bar(4)`


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:

Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...


The sum or difference of two G.P.s, is again a G.P.


If the sum of an infinite GP a, ar, ar2, ar3, ...... . is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, .... is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×