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# Ex.5.2 Q4 Arithmetic Progressions Solution - NCERT Maths Class 10

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## Question

Which term of the

\begin{align} \text{AP: 3, 8, 13, 18……. is 78.}\end{align}

Video Solution
Arithmetic Progressions
Ex 5.2 | Question 4

## Text Solution

What is Known?

The AP with missing terms

What is Unknown?

Which term will be $$78.$$

Reasoning:

\begin{align}a_{n}=a+(n-1) d \end{align}

Steps:

The AP is \begin{align} 3, 8, 13, 18. \end{align}

First term \begin{align} a &= 3 \end{align}

Second term \begin{align} a +d &= 8 \end{align}

Common difference \begin{align} d &= 8-3 = 5 \end{align}

\begin{align} a_{n}&= a+(n-1) d=78 \\ 3+(n-1) 5&=78 \\5(n-1)&=78-3 \\ n-1 &=15\\n&=16 \end{align}

$$78$$ is the $$16^\rm{th}$$ term of AP.

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