Maths / Arithmetic Progression / General Term Of an AP

QUESTION

Which of the following cannot be the nth term of an AP? Justify your answer.

$\dpi{120} \fn_jvn \large (a)\;\; 2n+1\;\;\;\; (b) 7-\frac{2}{3}n$

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large (a)\;\; 2n+1$

$\dpi{120} \fn_jvn \large a_1= 2(1)+1 = 2+1 =3$

$\dpi{120} \fn_jvn \large a_2= 2(2)+1 = 4+1 =5$

$\dpi{120} \fn_jvn \large a_3= 2(3)+1 = 6+1 =7$

$\dpi{120} \fn_jvn \large d_1=a_2-a_1= 5-3=2$

$\dpi{120} \fn_jvn \large d_2=a_3-a_2= 7-5=2$

$\dpi{120} \fn_jvn \large as\; d_1=d_2 \; So\;it\;is\;an\;AP$

$\dpi{120} \fn_jvn \large (b) 7-\frac{2}{3}n$

$\dpi{120} \fn_jvn \large a_1= 7-\frac{2}{3} (1)=7-\frac{2}{3} =\frac{21-2}{3}= \frac{19}{3}$

$\dpi{120} \fn_jvn \large a_2= 7-\frac{2}{3} (2)=7-\frac{4}{3} =\frac{21-4}{3}= \frac{17}{3}$

$\dpi{120} \fn_jvn \large a_3= 7-\frac{2}{3} (3)=7-2 =5$

$\dpi{120} \fn_jvn \large d_1=a_2-a_1= \frac{17}{3}-\frac{19}{3}= -\frac{2}{3}$

$\dpi{120} \fn_jvn \large d_2=a_3-a_2= 5-\frac{17}{3}=\frac{15-17}{3}=-\frac{2}{3}$

$\dpi{120} \fn_jvn \large as\; d_1=d_2 \; So\;it\;is\;an\;AP$

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