Question

Is 127 a term in the arithmetic progreession 15, 18, 21, 24.....

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{No\:Term\:of\:this\:A.P.\:is\:127\:.}}\:\:\star}$

Explanation :

Given :–

• 15 , 18 , 21 ,... are in A.P.
• where a = 15 and d = 3 .

To Check :–

• 127 is a Term of this A.P. ?

Formula Applied :–

• $\boxed{\star\:\:\bf{a_n\:=\:a\:+\:(n\:-\:1)d}\:\:\star}$

Solution :–

We have ,

• a = 15
• d = 3
• aₙ = 127 .

Putting these values in the Formula :

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

$\rightarrow\sf{127\:=\:15\:+\:(n\:-\:1)(3)}$

$\rightarrow\sf{127\:-\:15\:=\:3n\:-\:3}$

$\rightarrow\sf{112\:+\:3\:=\:3n}$

$\rightarrow\sf{115\:=\:3n}$

$\rightarrow\sf{n\:=\:\dfrac{115}{3} }$

$\rightarrow\sf{n\:=\:38.333\:... }$

So , the value of n is not definite .

∴ 127 is not a Term of this A.P.