Question

The nth term of an arithmetic progression is an

= 4n + 5 then the 3rd term is :​

Answer 1

Given :-

→ $\sf{n^{th}}$ term of the AP = 4n +5

To find :-

$\sf{3^{rd}}$  term of the AP

Solution :-

Let $\sf{t_{n}}$ denote the $\sf{n^{th}}$  term of the sequence

$\sf{t_{n}= 4n + 5}$  

So, first term = $\sf{t_{1}}$ $\sf{= 4(1)+5 = 9}$

Second term =  $\sf{t_{2} = 4(2) + 5 = 13}$

Third term = $\sf{t_{3} = 4(3) + 5 = 17 }$

               $\boxed{\sf{t_{3} = 17 }}$

$\bold{3^{rd} \ term \ of \ the \ AP = 17}$

Answer 2

Question :- The nth term of an arithmetic progression is an=4n+5 then the 3rd term is ?

Solution :-

we know that,

• nth term of an AP = a + (n - 1)d
• a = first term .
• d = common difference .

so,

→ a + (n - 1)d = 4n + 5

→ a + (n - 1)d = 4n - 4 + 4 + 5

→ a + (n - 1)d = 9 + 4n - 4

→ a + (n - 1)d = 9 + (n - 1)4

comparing we get,

• a = 9
• d = 4

therefore,

→ a3 = a + (3 - 1)d

→ a3 = 9 + 2*4

→ a3 = 9 + 8

→ a3 = 17 (Ans.)

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