Question

find the 100th term of an AP whose nth term is 3n+1​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If in an arithmetic progression

$\sf{ \: nth \: term = t_n}$

$\sf{Then \: {m} \: {th} \: term = t_m}$

GIVEN

In an arithmetic progression nth term is 3n+1

TO DETERMINE

100 th term of the arithmetic progression

CALCULATION

In the arithmetic progression n th term

$\sf{ t_n = 3n + 1}$

So the 100 th term of the arithmetic progression

$\sf{ \: t_{100} = (3 \times 100) + 1}$

$\implies \: \sf{ \: t_{100} = 300 + 1}$

$\sf{ \: t_{100} = 301}$

So the 100 th term of the arithmetic progression is 301

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Answer 2

Step-by-step explanation:

$\rm \bold{We \: have,}$

$\sf a_n = 3n+1$

$\bf Put \: n=100$

$\sf a_{100}=3(100)+1$

$\sf a_{100}=301$