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

large s_n = frac{n}{2}(2a+(n-1)d)

large frac{n}{2}(2(3)+(n-1)3)= 108

large frac{n}{2}(6+3n-3)= 108

large n(3+3n)= 108 X 2

large 3n^2 +3n - 216= 0

large n^2 +n - 72= 0

large n^2 +9n -8n- 72= 0

large n(n+9) -8(n +9)= 0

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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