| The average of the first nine integral multiples of 3 is [SSC (CGL) 2013] |
A) 12
B) 15
C) 18
D) 21
Correct Answer: B
Solution :
| By using arithmetic series |
| Sum of first 9 integral multiples of 3 |
| \[{{S}_{n}}=\frac{n}{2}[2a+(n-1)\,d]\] |
| where, \[n=9,\]\[a=3\] and \[d=3\] |
| \[\therefore \] \[{{S}_{n}}=\frac{9}{2}[2\times 3+(9-1)\,3]=\frac{9}{2}\times 30=135\] |
| \[\therefore \] Average \[=\frac{135}{9}=15\] |
| Alternate Method |
| Average of n multiples of any number |
| \[=\frac{\text{Number}\times (n+1)}{2}=\frac{3\times (9+1)}{2}=\frac{3\times 10}{2}=15\] |
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