Given is an A.P. in which -
- First term,a = 2
- Common difference = Second term - First term
[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1[/tex]
[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2 [/tex]
[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5[/tex]
Solution:-
nth term of an A.P ,is given by-
[tex]\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}[/tex]
where
- [tex]a_n = nth \;term[/tex]
- a = first term
- n = number of term
- d = common difference
Putting n = 46
[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, the 46th term is 227
