Question

write the formula for nth term of an A.P​

Answer 1

Answer:

The nth term of an AP can be found by the formula

Tn = a + (n-1)d

where, Tn is nth term of the AP

a is the first term of the AP

n is the total number of terms is the AP

and d is the common difference.

Answer 2

${\fcolorbox{black}{black}{\orange{Here's\:the\:Answer\:»»»}}}$

$\boxed{\text{Formula of nth term of AP}\leadsto}$

$\boxed{\boxed{\sf{\red{a_n \:=\: a\:+\:(\:n\:-\:1\:) \times d}}}}$

Example :

• Find the $\sf{15^{th}}$ term of an AP = 2 , 4 , 6 . . . . . . . . $\infty$

ㅤㅤ➪ Solution :

ㅤㅤㅤ➪ $\sf{a_1}$ = 2

ㅤㅤㅤ➪ $\sf{a_2}$ = 4

ㅤㅤㅤ➪ d = $\sf{a_2 \:-\: a_1}$

ㅤㅤㅤ➪ d = 4 - 2

ㅤㅤㅤ➪ d = 2

ㅤㅤ$\therefore \sf{15^{th}}$ term of the AP is

ㅤㅤ➪ $\sf{a_{15} \:=\: a \: +\: ( n - 1 ) \times d }$

ㅤㅤ➪ $\sf{a_{15} \:=\: 2 \:+\: ( 15 - 1 ) \times 2}$

ㅤㅤ➪ $\sf{a_{15} \:=\: 2\:+\: 30 \:-\: 2 }$

ㅤㅤ➪ $\sf{a_{15} \:=\: 32\:-\: 2}$

ㅤㅤ➪ $\sf{a_{15} \:=\: 30}$

MORE TO KNOW ::

• Sum of nth term

ㅤㅤ➪ $\orange{\boxed{\gray{\boxed{\green{\boxed{\sf{\blue{ \dfrac{n}{2} \:[ 2a \:+\: ( n - 1 ) \times d] }}}}}}}}$

ㅤㅤㅤ

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂