Verify that each of the following lists of numbers is an A.P., and the write its next three terms: (i) \[\mathbf{0},\text{ }{\scriptscriptstyle 1\!/\!{ }_4},\text{ }{\scriptscriptstyle 1\!/\!{ }_2},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }\ldots \] (ii) \[\mathbf{5},\text{ }\mathbf{14}/\mathbf{3},\text{ }\mathbf{13}/\mathbf{3},\text{ }\mathbf{4},\text{ }\ldots \]

Verify that each of the following lists of numbers is an A.P., and the write its next three terms: (i)

$\mathbf{0},\text{ }{\scriptscriptstyle 1\!/\!{ }_4},\text{ }{\scriptscriptstyle 1\!/\!{ }_2},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }\ldots$

(ii)

$\mathbf{5},\text{ }\mathbf{14}/\mathbf{3},\text{ }\mathbf{13}/\mathbf{3},\text{ }\mathbf{4},\text{ }\ldots$

Verify that each of the following lists of numbers is an A.P., and the write its next three terms: (i)

$\mathbf{0},\text{ }{\scriptscriptstyle 1\!/\!{ }_4},\text{ }{\scriptscriptstyle 1\!/\!{ }_2},\text{ }{\scriptscriptstyle 3\!/\!{ }_4},\text{ }\ldots$

(ii)

$\mathbf{5},\text{ }\mathbf{14}/\mathbf{3},\text{ }\mathbf{13}/\mathbf{3},\text{ }\mathbf{4},\text{ }\ldots$

From the question it is given that,

First term a = 0

Common difference

$=\text{ }{\scriptscriptstyle 1\!/\!{ }_4}\text{ }\text{ }0\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_4}$

So, next three numbers are

${\scriptscriptstyle 3\!/\!{ }_4}\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_4}\text{ }=\text{ }4/4\text{ }=\text{ }1$

$\begin{array}{*{35}{l}} 1\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_4}\text{ }=\text{ }\left( 4\text{ }+\text{ }1 \right)/4\text{ }=\text{ }5/4 \\ 5/4\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_4}\text{ }=\text{ }6/4\text{ }=\text{ }3/2 \\ \end{array}$

Therefore, the next three term are

$1,\text{ }5/4\text{ }and\text{ }3/2$

(ii)

$\mathbf{5},\text{ }\mathbf{14}/\mathbf{3},\text{ }\mathbf{13}/\mathbf{3},\text{ }\mathbf{4},\text{ }\ldots$

Solution:-

From the question it is given that,

First term a =

$5$

Common difference =

$~14/3\text{ }\text{ }5\text{ }=\text{ }\left( 14\text{ }\text{ }15 \right)/3\text{ }=\text{ }-1/3$

So, next three numbers are

$4\text{ }+\text{ }\left( -1/3 \right)\text{ }=\text{ }\left( 12\text{ }\text{ }1 \right)/3\text{ }=\text{ }11/3$

$\begin{array}{*{35}{l}} 11/3\text{ }+\text{ }\left( -1/3 \right)\text{ }=\text{ }\left( 11\text{ }\text{ }1 \right)/3\text{ }=\text{ }10/3 \\ 10/3\text{ }+\text{ }\left( -1/3 \right)\text{ }=\text{ }\left( 10\text{ }\text{ }1 \right)/3\text{ }=\text{ }9/3\text{ }=\text{ }3 \\ \end{array}$

Therefore, the next three term are

$11/3,\text{ }10/3\text{ }and\text{ }3$

More Material

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

Two cells of emf $\varepsilon_{1}$ and $\varepsilon_{2}$ , internal resistance $r_{1}$ and $r_{2}$ , connected in parallel. The equivalent emf of the combination is- (A) $\frac{\varepsilon_{1} r_{1}+\varepsilon_{1} r_{1}}{r_{1}+r_{2}}$ (B) $\frac{\varepsilon_{1} r_{2}+\varepsilon_{2} r_{1}}{r_{1}+r_{2}}$ (C) $\sqrt{\varepsilon_{1} \times \varepsilon_{2}}$ (D) $\frac{\varepsilon_{1}+\varepsilon_{2}}{2}$

More Material

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

If the points $A(a, 0), B(0, b)$ and $C(1,1)$ are collinear, prove that $\frac{1}{a}+\frac{1}{b}=1$

If $A(-2,0), B(0,4)$ and $C(0, k)$ be three points such that area of a $A B C$ is 4 sq units, find the value of $k$ .

Find the value of $k$ for which the area of a ABC having vertices $A(2,-6), B(5,4)$ and $C(k, 4)$ is 35 sq units.

Find the value of $k$ for which the points $A(1,-1), B(2, k)$ and $C(4,5)$ are collinear.

Find the value of $k$ for which the points $P(5,5), Q(k, 1)$ and $R(11,7)$ are collinear.

Find the value of $k$ for which the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear.

Use determinants to show that the following points are collinear. $P(-2,5), Q(-6,-7)$ and $R(-5,-4)$

Sign up now and study all subjects for free

Class

Syllabus

Question Papers

Social Media

Apps