Question

Find the value of Tn if first two terms are 3 and 5 in AP and n = 101. ​

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• First and second terms are 3 , 5
• n = 101

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To find :

• Tn

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Solution :

AP is a series of numbers in which common difference between two consecutive terms is same.

Formula to find Tn is,

$\boxed{\sf\Longrightarrow Tn\:=\:a\:+\:(\:n\:-\:1\:)\:d}$

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Here,

• a = First term
• n = number of terms
• d = Common difference between two consecutive terms

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In order to find Tn, we must have the values of a, n and d out of which a and n are given in the question. We just have to find the common difference and substitute it in the above formula.

$\sf{ Common\: difference\:=\:2nd\:term\:-\:1st\:term}$

$\sf{Common\: difference\:=\:5\:-\:3}$

$\sf{ \purple{Common\: difference\:=\:2}}$

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Since we have obtained all the required values, now substitute them in formula.

$\sf{\longrightarrow \:Tn\:=\:a\:+\:(\:n\:-\:1\:)\:d\:}$

$\sf{\longrightarrow \:T101\:=\:3\:+\:(\:101\:-\:1\:)\:2\:}$

$\sf{\longrightarrow \:T101\:=\:3\:+\:(\:100\:)\:2\:}$

$\sf{\longrightarrow \:T101\:=\:3\:+\:200\:}$

$\sf{\longrightarrow \:T101\:=\:203\:}$

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Hence the required value of Tn is 203.