Maths / Arithmetic Progression / Find Number of Terms When Sum of N Terms, First Term and Common Difference are Given

QUESTION

How many terms of an AP series 3,6, 9, 12, 15 will sum up to 108

 OPTIONS A. 6 B. 9 C. 8 D. 7
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

a= 3, d = 3

$\dpi{120} \fn_jvn \large s_n = \frac{n}{2}(2a+(n-1)d)$

$\dpi{120} \fn_jvn \large \frac{n}{2}(2(3)+(n-1)3)= 108$

$\dpi{120} \fn_jvn \large \frac{n}{2}(6+3n-3)= 108$

$\dpi{120} \fn_jvn \large n(3+3n)= 108 X 2$

$\dpi{120} \fn_jvn \large 3n^2 +3n - 216= 0$

$\dpi{120} \fn_jvn \large n^2 +n - 72= 0$

$\dpi{120} \fn_jvn \large n^2 +9n -8n- 72= 0$

$\dpi{120} \fn_jvn \large n(n+9) -8(n +9)= 0$

$\dpi{120} \fn_jvn \large (n-8)(n+9)=0$

Either n = 8 or n = -9

As the number terms can not be negative so the value of n = 8

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