Maths / Arithmetic Progression / Finding The Value of N When Nth Term and AP is Given

QUESTION

What is the value of 9th term of an AP Series whose 6th term and 12th terms are 32 and 56, respectively?

 OPTIONS A. 42 B. 44 C. 34 D. None of these
Right Option : B

EXPLANATION
Explain TypeExplanation Content
Text

Given that ,6thg term $\dpi{80} \LARGE \left ( a_6 \right )=32$

$\dpi{80} \LARGE \Rightarrow a+(6-1)d=32$

$\dpi{80} \LARGE \Rightarrow a+5d=32$

and 12th term $\dpi{80} \LARGE \left ( a_1_ _2\right )56$

$\dpi{80} \LARGE \Rightarrow a+(12-1)d=56$

On adding Eqs.(1) and (2),we get

$\dpi{80} \LARGE \Rightarrow 2a=16d=88$

$\dpi{80} \LARGE \Rightarrow a+8d=44$

$\dpi{80} \LARGE \therefore a_9=a+(9-1)d$

=a+8d=44

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