Ex.5.2 Q1 Arithmetic Progressions Solution - NCERT Maths Class 10

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Question

Fill in the blanks in the following table, given that \(a\) is the first term and \(d\) is the Common difference and \(\begin{align}{a_n}\end{align}\) the \(n^{th}\) term of the AP.

\(a\) \(d\) \(n\) \(\begin{align}{a_n}\end{align}\)
7 3 8 …….
- 18 …….. 10 0
……. -3 18 -5
-18. 9 2.5 ……. 3.6
3.5 0 105 …….

 Video Solution
Arithmetic Progressions
Ex 5.2 | Question 1

Text Solution

 

i) Reasoning:

\(\begin{align}{a_n} = a + \left( {n - 1} \right)d\end{align}\)

What is Known?

\(a = 7,d = 3,n = 8\)

What is Unknown?

\(\begin{align}{a_n}\end{align}\)

Steps:

\[\begin{align}{a_n} &= a + (n - 1)d\\ {a_8} &= 7 + (8 - 1)3\\& = 7 + 7 \times 3\\& = 7 + 21\\& = 28 \end{align}\]

The Answer is \(a_n = 28\)

ii) What is Known?

\(a = - 18,\,{a_n} = 0,n = 10\)

What is Unknown?

\(d.\)

Steps:

\[\begin{align}a_n &= a + (n - 1)d\\ 0 &= - 18 + (10 - 1)d\\ 0 &= - 18 + 9d\\ 9d &= 18\\ d &= 2 \end{align}\]

The Answer is \(\begin{align}d = 2\end{align}\)

iii) What is Known?

\(d = -3, \,a_n = -5 , n = 18\)

What is Unknown?

\(a\)

Steps:

\[\begin{align} {a_n} &= a + (n - 1)d\\ - 5 &= a + (18 - 1)( - 3)\\ - 5 &= a + 17 \times ( - 3)\\ - 5 &= a - 51\\ a &= 51 - 5\\ a &= 46 \end{align}\]

The Answer is \(a = 46\)

iv) What is Known?

\({a_n} = 3.6\,,d = 2.5\,,a = - 18.9\)

What is Unknown?

\(\begin{align}n. \end{align}\)

Steps:

\[\begin{align} {a_n}& = a + (n - 1)d\\ 3.6 &= - 18.9 + (n - 1)2.5\\ 3.6 + 18.9 &= 2.5(n - 1)\\ 22.5& = 2.5(n - 1)\\ n - 1 &= \frac{{22.5}}{{2.5}}\\ n - 1 &= \frac{{225}}{{25}}\\ n - 1 &= 9\\ n& = 10 \end{align}\]

The Answer is \(n = 10\)

v) What is Known?

\(a = 3.5,d = 0,n = 105\)

What is Unknown?

\(\begin{align}{a_n}\end{align}\)

Steps:

\[\begin{align} {a_n} &= a + (n - 1)d\\ {a_n} &= 3.5 + (105 - 1)(0)\\ {a_n} &= 3.5 + 104 \times 0\\ {a_n} &= 3.5 \end{align}\]

The Answer is \(a_n = 3.5\)