Question
Identify the following sequence is in G.P.?
$16,4,1, \frac{1}{4}, \ldots$
$16,4,1, \frac{1}{4}, \ldots$
✓
Answer
$16,4,1, \frac{1}{4}, \ldots $
$r =\frac{ t _2}{ t _1}=\frac{4}{16}=\frac{1}{4} $
$r =\frac{ t _3}{ t _2}=\frac{1}{4} $
$r =\frac{1}{4}=\frac{1}{4}$
$\therefore$ It is a G.P.
$r =\frac{ t _2}{ t _1}=\frac{4}{16}=\frac{1}{4} $
$r =\frac{ t _3}{ t _2}=\frac{1}{4} $
$r =\frac{1}{4}=\frac{1}{4}$
$\therefore$ It is a 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.
Explore more
Similar questions
4 persons live in a conical tent whose slant height is 19 cm. If each person requires 22 cm$^2$ of the floor area, then find the height of the tent
→If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P(A ∪ B) = 0.65, then find P(B).
Find the square root of the following rational expression
$
\frac{7 x^2+2 \sqrt{14} x+2}{x^2-\frac{1}{2} x+\frac{1}{16}}
$
→$
\frac{7 x^2+2 \sqrt{14} x+2}{x^2-\frac{1}{2} x+\frac{1}{16}}
$
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
$D$ is the mid point of side $B C$ and $A E \perp B C$. If $B C=a, A C=b, A B=c, E D=x, A D=p$ and $A E=$ $h$, prove that $b^2+c^2=2 p^2+\frac{a^2}{2}$
→If $a \cos \theta-b \sin \theta=c$, then prove that $(a \sin \theta+b \cos \theta)= \pm \sqrt{a^2+b^2-c^2}$
→Show that 107 is of the form 4q +3 for any integer q
The frustum shaped outer portion of the table lamp has to be painted including the top part. Find the total cost of painting the lamp if the cost of painting 1 sq.cm is ₹ 2.
A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter
Determine the quadratic equation, whose sum and product of roots are $\frac{-3}{2},-1$
→