In an A.P., the fourth and sixth terms are \[8\] and \[14\], respectively. Find the: (i) first term (ii) common difference - Noon Academy

In an A.P., the fourth and sixth terms are

$8$

and

$14$

, respectively. Find the: (i) first term (ii) common difference

Arithmetic and Geometric Progression | Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal

In an A.P., the fourth and sixth terms are

$8$

and

$14$

, respectively. Find the: (i) first term (ii) common difference

From the question it is given that,

${{T}_{4}}~=\text{ }8\text{ }and\text{ }{{T}_{6}}~=\text{ }14$

⇒

$a\text{ }+\text{ }3d\text{ }=\text{ }8$

… (i)

⇒

$a\text{ }+\text{ }5d\text{ }=\text{ }14$

… (ii)

Subtracting (i) from (ii), we get

$\begin{array}{*{35}{l}} \left( a\text{ }+\text{ }5d \right)\text{ }\text{ }\left( a\text{ }+\text{ }3d \right)\text{ }=\text{ }14\text{ }\text{ }8 \\ 5d\text{ }\text{ }3d\text{ }=\text{ }6 \\ 2d\text{ }=\text{ }6 \\ d\text{ }=\text{ }6/2 \\ d\text{ }=\text{ }3 \\ \end{array}$

(ii) Hence, common difference d =

$3$

Substituting the value of d in (i), we have

$\begin{array}{*{35}{l}} a\text{ }+\text{ }3\left( 3 \right)\text{ }=\text{ }8 \\ a\text{ }=\text{ }8\text{ }\text{ }9 \\ a\text{ }=\text{ }-1 \\ \end{array}$

(i) Hence, the first term =

$-1$

i

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) $\frac{\varepsilon_{1}+\varepsilon_{2}}{2}$

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 $R(-5,-4)$

← Previous Next →