Question

which term of the A.P. 21, 42,63, 84, .... is 231 ?

Answer 1

a1= 21

a2= 42

d= @2-@1

=) 42-21

)) 21

an=) 231

an= a+(n-1) d

231 =21+ (n-1) 21

231- 21= 21n - 21

231-21+21=21n

231/21=) n

N = 11

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Answer 2

$\sf{Given \ :}$



$\sf{AP \ : \ 21, \ 42, \ 63, \ 84, \ .......}$



$\sf{a_n \ = \ 231}$



$\sf{Here,}$



$\sf{a \ = \ 21}$



$\sf{a_2 \ = \ 42}$



$\sf{d \ = \ a_2 - a \ = \ 42 - 21 \ = \ 21}$



$\sf\red{Using \ formula \ -}$



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



$\sf{231 \ = \ 21 + ( \ n - 1 \ ) \ 21}$



$\sf{231 - 21 \ = \ ( \ n - 1 \ ) \ 21}$



$\sf{210 \ = \ ( \ n - 1 \ ) \ 21}$



$\sf{( \ n - 1 \ ) \ = \ {\dfrac{210}{21}}}$



$\sf{( \ n - 1 \ ) \ = \ 10}$



$\sf{n \ = \ 10 + 1}$



$\sf{n \ = \ 11}$



$\sf{Hence,}$



$\sf\blue{11th \ term \ of \ AP \ is \ 231.}$