Question

find the 100th term of : 4, 7, 10,.........

Answer 1

a+(n-1)d
4+99*3= 4+297=301

Answer 2

${\large{\mathfrak{\underline{\underline{Solution :}}}}}$

$\sf{A.P.\:=\:4,\:7,\:10,\:.....}$

$\sf{First \ Term, \ a \ = \ 4}$

$\sf{Second \ Term, \ a_2 \ = \ 7}$

${\boxed{\sf{Common \ Difference, \ d \ = \ a_2 - a}}}$

$\sf{d \ = \ 7 - 4 \ = \ 3}$

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

$\sf{Here, \ n \ = \ 100}$

$\sf{100th \ Term \ -}$

$\sf{{a}_{100} \ = \ 4 + (100 - 1)3}$

$\sf{{a}_{100} \ = \ 4 + (99)3}$

$\sf{{a}_{100} \ = \ 4 + 297}$

$\sf{{a}_{100} \ = \ 301}$

$\sf{Hence, \ 100th \ Term \ is \ 301.}$