Maths / Arithmetic Progression / General Term Of an AP

QUESTION

For an AP, if 6 times the 6th term is equal to 9 times the 9th term, then the value of 15th term is ____________

 OPTIONS A. 15 B. 14 C. 0 D. cannot be calculated
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large \dpi{120} \fn_jvn \large \dpi{120} \fn_jvn \large a_6=a+(6-1)d=a+5d$

$\dpi{120} \fn_jvn \large a_9=a+(9-1)d=a+8d$

A.T.Q.

$\dpi{120} \fn_jvn \large 6\; X \;a_6= 9 \;X\;a_9$

$\dpi{120} \fn_jvn \large 6(a+5d)= 9(a+8d)$

$\dpi{120} \fn_jvn \large 6a+30d= 9a+72d$

$\dpi{120} \fn_jvn \large 6a+30d - 9a-72d =0$

$\dpi{120} \fn_jvn \large -3a-42d =0$

$\dpi{120} \fn_jvn \large -3(a+14d) =0$

$\dpi{120} \fn_jvn \large a+14d =0$

$\dpi{120} \fn_jvn \large a_{15} =0$

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