Advertisements
Advertisements
Question
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
Advertisements
Solution
Let the required numbers be G1 and G2.
∴ 5, G1, G2, 40 are in G.P.
∴ t1 = 5, t2 = G1, t3 = G2, t4 = 40
∴ t1 = a = 5, t4 = 40
tn = arn–1
∴ t4 = 5(r)4–1
∴ 40 = 5r3
∴ r3 = 8 = 23
∴ r = 2
G1 = t2 = ar = 5 (2) = 10
G2 = t3 = ar2 = 5(2)2 = 20
∴ For resulting sequence to be in G.P. we need to insert numbers 10 and 20.
APPEARS IN
RELATED QUESTIONS
Which term of the following sequence:
`1/3, 1/9, 1/27`, ...., is `1/19683`?
Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
Find the value of n so that `(a^(n+1) + b^(n+1))/(a^n + b^n)` may be the geometric mean between a and b.
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.
Show that one of the following progression is a G.P. Also, find the common ratio in case:
\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
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 series:
`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;
Find the sum of the following series:
0.6 + 0.66 + 0.666 + .... to n terms
If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.
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 a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If a, b, c, d are in G.P., prove that:
(a2 − b2), (b2 − c2), (c2 − d2) are in G.P.
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.
If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is
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.
7, 14, 21, 28, …
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Find GM of two positive numbers whose A.M. and H.M. are 75 and 48
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
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:
For a G.P. a = `4/3` and t7 = `243/1024`, find the value of r
Answer the following:
If for a G.P. t3 = `1/3`, t6 = `1/81` find r
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.
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.
The third term of G.P. is 4. The product of its first 5 terms is ______.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
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 ______.
