Question

find the 10th term of AP:-x,,4x/3,,5x/3,,,2x........​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{A.P\;is\;x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}$

$\underline{\textbf{To find:}}$

$\mathsf{10\,th\;term\;of\;the\;x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}$

$\mathsf{Here,\;first\;term,a=x}$

$\mathsf{Here,\;common\;difference,\;d=t_2-t_1=\dfrac{4x}{3}-x=\dfrac{x}{3}}$

$\textbf{10 th term of the A.P}$

$\mathsf{=t_{10}}$

$\mathsf{=a+9d}$

$\mathsf{=x+9\left(\dfrac{x}{3}\right)}$

$\mathsf{=x+3x}$

$\mathsf{=4\,x}$

$\implies\boxed{\bf\,t_{10}=4\,x}$

$\underline{\textbf{Answer:}}$

$\textbf{10 th term of the A.P is 4x}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{8cm} \\\textsf{The n th term of the A.P, a, a+d, a+2d, . . . . .is}\\\\\mathsf{t_n=a+(n-1)d}\\ \end{minipage}}$

Answer 2

Step-by-step explanation:

\underline{\textbf{Given:}}

Given:

\mathsf{A.P\;is\;x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}A.Pisx,

3

4x

,

3

5x

,2x......

\underline{\textbf{To find:}}

To find:

\mathsf{10\,th\;term\;of\;the\;x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}10thtermofthex,

3

4x

,

3

5x

,2x......

\underline{\textbf{Solution:}}

Solution:

\mathsf{Consider,}Consider,

\mathsf{x,\dfrac{4x}{3},\dfrac{5x}{3},2x\;.\;.\;.\;.\;.\;.}x,

3

4x

,

3

5x

,2x......

\mathsf{Here,\;first\;term,a=x}Here,firstterm,a=x

\mathsf{Here,\;common\;difference,\;d=t_2-t_1=\dfrac{4x}{3}-x=\dfrac{x}{3}}Here,commondifference,d=t

2

−t

1

=

3

4x

−x=

3

x

\textbf{10 th term of the A.P}10 th term of the A.P

\mathsf{=t_{10}}=t

10

\mathsf{=a+9d}=a+9d

\mathsf{=x+9\left(\dfrac{x}{3}\right)}=x+9(

3

x

)

\mathsf{=x+3x}=x+3x

\mathsf{=4\,x}=4x

\implies\boxed{\bf\,t_{10}=4\,x}⟹

t

10

=4x

\underline{\textbf{Answer:}}

Answer:

\textbf{10 th term of the A.P is 4x}10 th term of the A.P is 4x

\underline{\textbf{Formula used:}}

Formula used:

\begin{gathered}\boxed{\begin{minipage}{8cm}$\\\textsf{The n th term of the A.P, a, a+d, a+2d, . . . . .is}\\\\\mathsf{t_n=a+(n-1)d}\\$\end{minipage}}\end{gathered}