Question

2,7, 12, ... Find the 46th term.

Answer 1

Given is an A.P. in which -

• First term,a = 2
• Common difference = Second term - First term

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1$

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2$

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5$

Solution:-

nth term of an A.P ,is given by-

$\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}$

where

• $a_n = nth \;term$
• a = first term
• n = number of term
• d = common difference

Putting n = 46

$\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered}$

$\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered}$

$\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered}$

$\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered}$

$\longrightarrow$Therefore, the 46th term is 227