Maths / Arithmetic Progression / Find Last Term When First Term, Number of Terms and Sum of N Terms is Given

QUESTION

Find the 6th term of an AP whose first trem  $\dpi{120} \fn_jvn \large 2x^2+2x-4$ and sum of 6 terms is $\dpi{120} \fn_jvn \large 6x^2-x-4$

 OPTIONS A. $\dpi{120} \fn_jvn \large \frac{ -7x+8}{3}$ B. $\dpi{120} \fn_jvn \large \frac{ -7x+16}{3}$ C. $\dpi{120} \fn_jvn \large \frac{ -5x+8}{3}$ D. $\dpi{120} \fn_jvn \large \frac{ -5x-16}{3}$
Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large S_n = \frac{n}{2}(a+l)$

$\dpi{120} \fn_jvn \large 6x^2-x-4 = \frac{6}{2}(2x^2+2x-4 +l)$

$\dpi{120} \fn_jvn \large 6x^2-x-4 = 3(2x^2+2x-4 +l)$

$\dpi{120} \fn_jvn \large 6x^2-x-4 = 6x^2+6x-12 +3l$

$\dpi{120} \fn_jvn \large 3l = 6x^2-x-4 - 6x^2-6x+12$

$\dpi{120} \fn_jvn \large 3l = -7x+8$

$\dpi{120} \fn_jvn \large l =\frac{ -7x+8}{3}$

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