Maths / Arithmetic Progression / General Term Of an AP

QUESTION

The fourth term of an AP is 0. What is the relationship between its 25th term and its 11th term.

 OPTIONS A. Equal B. Double C. Triple D. Four Times
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large a_n=a+(n-1)d =0$

$\dpi{120} \fn_jvn \large a_4=a+(4-1)d = a+3d$

A.T.Q.

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

$\dpi{120} \fn_jvn \large a_{25}=a+24d$

$\dpi{120} \fn_jvn \large a_{11}=a+10d$

A.T.Q.

$\dpi{120} \fn_jvn \large \dpi{120} \fn_jvn \large a_{25}= m Xa_{11}$

$\dpi{120} \fn_jvn \large a+ 24d= m(a+10d)$

$\dpi{120} \fn_jvn \large \frac{a+ 24d}{a+10d}=m$

$\dpi{120} \fn_jvn \large \frac{a+ 3d+21d}{a+3d+7d}=m$

According to equation I

a+3d=0

$\dpi{120} \fn_jvn \large \frac{0+21d}{0+7d}=m$

$\dpi{120} \fn_jvn \large \frac{21d}{7d}=m$

$\dpi{120} \fn_jvn \large 3=m$

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