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.