Ex.5.2 Q2 Arithmetic Progressions Solution - NCERT Maths Class 10

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Question

Choose the correct choice in the following and justify:

i) \(30^{th}\) term of the \(\begin{align}\text{AP: 10,7,4……. is}\end{align}\)

\(\begin{align}\text{a) 97 } \qquad \text{b) 77 }\qquad \text{c) }-77 \qquad \text{d) }-87\end{align}\)

ii) \(11^{th}\) term of \(\begin{align}\text{AP: }-3, - \frac{1}{2},2\, \rm{is:}\end{align}\)

\(\begin{align}\text{a) 28}\qquad \text{b) 22 } \qquad \text{c) }– 38 \qquad \text{d) }- 48\frac{1}{2}\end{align}\)

 Video Solution
Arithmetic Progressions
Ex 5.2 | Question 2

Text Solution

 

Reasoning:

\(n^{th}\) term of a AP is \(\begin{align}\,{a_n} = a + \left( {n - 1} \right)d\end{align}\)

i)  What is  Known?

The AP.

What is Unknown?

\(30^{th}\) term of the AP.

Steps:

The AP is \(10,7,4, …..\)

\[\begin{align}a = 10\end{align}\]

\[\begin{align} \text { Common difference } &=a_{2}-a_{1} \\ &=7-10 \\ &=-3 \end{align}\]

\[\begin{align}{a_n} &= a + (n - 1)d\\{a_{30}} &= 10 + (30 - 1)( - 3)\\ &= 10 + (29)( - 3)\\ &= 10 - 87\\ &= - 77\end{align}\]

The correct option is \(\begin{align}c = -77\end{align}\)

\(30^{th}\) term is \(\begin{align}-77.\end{align}\)

ii)  What is  Known?

The AP.

What is Unknown?

\(11^{th}\) term of the AP.

Steps:

The AP is -3,\(\begin{align} - \frac{1}{2}\end{align}\) , \(2\)

\[\begin{align} \text { Common difference d } &=a_{2}-a_{1} \\ &=-\frac{1}{2}-(-3) \\ &=-\frac{1}{2}+3 \\ &=\frac{-1+6}{2} \\ d &=\frac{5}{2} \end{align}\]

\[\begin{align}{a_{11}} &= - 3 + (11 - 1)\frac{5}{2}\\ &= - 3 + 10 \times \frac{5}{2}\\ &= - 3 + 25\\{a_{11}} &= 22\end{align}\]

The correct option is B. \(11^{th}\) term is \(22.\)