Insert three numbers between 1 and 256 so that the resulting sequ… - Vidyadip

Question

Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.

✓

Answer

Suppose $G_1, G_2, G_3$ be three numbers between 1 and 256 such that $1, G_1, G_2, G_3, 256$ is a G.P.
Thus, $256=r^4$ giving $r= \pm 4$ (Taking real roots only)
For $r=4$, we have $G_1=a r=4, G_2=a r^2=16, G_3=a r^3=64$
Similarly, for $r=-4$, numbers are $-4,16$ and -64
Therefore, we can insert $4,16,64$ between 1 and 256 so that the resulting sequences are in G.P.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from SEQUENCES AND SERIES→SEQUENCES AND SERIES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If P(n) is the statement "n(n + 1) is even", then what is P(3)?

Check whether the following statement are true or not: p: If x and y are odd integers, then x + y is an even integer.

Write the first five terms of the sequence whose $n^{th}$ term is $a_n = 2^n$

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$ $\frac{-5\pi}{6}$

If x $\in$A and A $\in$B , then x $\in$B.If it is true, prove it. If it is false, give an example.

Write down the all possible proper subset of the given set.
{1, 2, 3}

If $\text{f(x)}=1-\frac{1}{\text{x}},$ then write the value of $\text{f}\Big(\text{f}\Big(\frac{1}{\text{x}}\Big)\Big)$

Show that the statement: p : "If x is a real number such that $x ^3+ x =0$, then x is $0^{\text {" }}$ is true by. Method of contradition.

Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x + 5 = 8}

{a} $\subset${a, b, c}