Question

which term of A.P:21,42,63,84___​

Answer 1

Solution :-

Given Arthemetic Progressions to us is

➤ 21 , 42 , 63 , 84 , ____

We are required to find next term , and we can solve it by two methods .

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } MethoD\:1:-}}}}}$

The AP is 21 , 42 , 63 , 84 , ____

The common difference is 42 - 21 = $\red{\sf 21 }$ . So , the next will be obtained by adding common difference to the previous term .

Here that previous term is 84 . So , next term would be ;

= $\tt 84 + 21$

= $\boxed{\purple{\bf 105 }}$

__________________________________

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } MethoD\:2:-}}}}}$

Here we will use the formula to find the nth term of AP when first term common difference and n is given .

$\tt Here , the \:terms\:are$

• $\sf First \:term= 21$
• $\sf Common\: Difference=21$
• $\sf nth \:term = 5$

$\bf \qquad\qquad \underline{\boxed{\bf The\: formula\:is}}$

$\large{\boxed{\red{\bf \green{\dag}\:T_n\:=\:a+(n-1)d}}}$

$\tt Using\: this\: formula$

$\tt :\implies T_n=a+(n-1)d$

$\tt :\implies T_5= 21+(5-1)21$

$\tt :\implies T_5 = 21+4\times21$

$\tt :\implies T_5=21+84$

$\underline{\boxed{\red{\tt{\longmapsto\:Term_5\:\:=105}}}}$

$\boxed{\green{\pink{\dag}\: \sf Hence\:the\: required\: term \:is\:105.}}$

Answer 2

Solution :

we need to use the formula to find the nth term of AP when first term common difference and n is given .

$\tt { Here \:, the \:terms\:are : 21 , 42 , 63 , 84 ,....}$

$\bold \tt { First \:term= 21}$

$\bold \tt {Common\:Difference=21}$

$\bold \tt {nth \:term = 5}$

$\bf{ Formula\: used \:is}$$\large{\boxed{\tt{\:a_n\:=\:a+(n-1)d}}}$

$\tt {Putting \: the \: values \: in \: the \: formula :}$

$\tt :\implies { a_n=a+(n-1)}$

$\tt :\implies {a_5= 21+(5-1)21 }$

$\tt :\implies {a_5 = 21+4 \times 21}$

$\tt :\implies {a_5=21+84}$

$\underline{\boxed{\tt{\: a_5\:\:=105}}}$

$\boxed {\bf {Hence\:the\: required\: term \:is\:105.}}$