Advertisements
Advertisements
प्रश्न
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]
Advertisements
उत्तर
Since the current worth of the house is ₹ 15 Lac and it appreciates 5% per year, the value of the house in every successive year form a G.P. with a = 15 Lac and r = `1 + 5/100` = 1.05
∴ value of the house after 6 years
= t7 = ar7–1
= 15(1.05)6
= 15 × 1.34
= 20.1 Lac
APPEARS IN
संबंधित प्रश्न
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
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.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]
Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.
Which term of the G.P. :
\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, \frac{1}{4\sqrt{2}}, . . . \text { is }\frac{1}{512\sqrt{2}}?\]
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
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 geometric progression:
1, −1/2, 1/4, −1/8, ... to 9 terms;
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 series:
7 + 77 + 777 + ... to n terms;
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?
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.
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If a, b, c, d are in G.P., prove that:
(a2 − b2), (b2 − c2), (c2 − d2) are in G.P.
If a, b, c are three distinct real numbers in G.P. and a + b + c = xb, then prove that either x< −1 or x > 3.
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
Write the product of n geometric means between two numbers a and b.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
The fractional value of 2.357 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
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
The numbers 3, x, and x + 6 form are in G.P. Find x
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
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.
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`
Express the following recurring decimal as a rational number:
`2.bar(4)`
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 –
Select the correct answer from the given alternative.
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
If pth, qth, and rth terms of an A.P. and G.P. are both a, b and c respectively, show that ab–c . bc – a . ca – b = 1
Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______.
