A) 205
B) 225
C) 238
D) 241
Correct Answer: D
Solution :
| [d] Let |
| \[\begin{align} & S=3+7+13+21+31+.....+{{a}_{n}} \\ & -S=\_3\pm 7\pm 13\pm 21\pm 31\pm ...\pm {{a}_{n}}\pm {{a}_{n}} \\ & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ & 0=3+4+6+8+10+12+....-{{a}_{n}} \\ \end{align}\] |
| \[\Rightarrow \,\,{{a}_{n}}=3+[4+6+8+10+12+...(n-1)\,terms]\] |
| \[=3+\frac{(n-1)}{2}[8+\{(n-1)-1\}\times 2]\] |
| \[=3+\frac{(n-2)}{2}[8+2n-4]\] |
| \[=3+\frac{(n-2)}{2}[2n+4]\] |
| \[=3+(n-1)\,(n+2)\] |
| \[\therefore \] 15th term \[={{a}_{15}}=3+(15-1)\,(15+2)\] |
| \[=3+14\times 17=241\] |
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