Advertisements
Advertisements
प्रश्न
Find:
the 10th term of the G.P.
\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]
उत्तर
Here,
\[\text { First term }, a = \frac{- 3}{4} \]
\[\text { Common ratio, } r = \frac{a_2}{a_1} = \frac{\frac{1}{2}}{- \frac{3}{4}} = - \frac{2}{3}\]
\[ \therefore 10th \text { term }= a_{10} = a r^{(10 - 1)} = \left( \frac{- 3}{4} \right) \left( \frac{- 2}{3} \right)^9 = \frac{1}{2} \left( \frac{2}{3} \right)^8 \]
\[\text { Thus, the 10th term of the given GP is } \frac{1}{2} \left( \frac{2}{3} \right)^8 .\]
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
Evaluate `sum_(k=1)^11 (2+3^k )`
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
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 two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.
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.
Find the 4th term from the end of the G.P.
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 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
Find the sum of the following series:
0.5 + 0.55 + 0.555 + ... to n terms.
The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.
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.
Express the recurring decimal 0.125125125 ... as a rational number.
Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
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 xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
Find the geometric means of the following pairs of number:
−8 and −2
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.
If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
For the following G.P.s, find Sn
3, 6, 12, 24, ...
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
9, 8.1, 7.29, ...
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
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 -
Answer the following:
Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
The third term of a G.P. is 4, the product of the first five terms is ______.
