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Sum of n Terms

If sum of fir...

Question

If sum of first $n$ terms of an $A P$ (having positive terms) is given by $S_{n} = (1 + 2 T_{n}) (1 - T_{n})$ , where $T_{n}$ is the $n t h$ terms of the series, and $T_{2}^{2} = \frac{\sqrt{a} - \sqrt{b}}{4} (a, b ϵ N)$ . Then $(a + b)$ is

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Solution

$T_{1} = a, T_{2} = a + d S_{n} = (1 + 2 T_{n}) (1 - T_{n}) S_{1} = T_{1} = (1 + 2 T_{1}) (1 - T_{1}) T_{1} = 1 + T_{1} - 2 T_{1}^{2} T_{1} = \frac{1}{\sqrt{2}} S_{2} = T_{2} + T_{1} = (1 + 2 T_{2}) (1 - T_{2}) T_{2} + T_{1} = 1 + T_{2} - 2 T_{2}^{2} 2 T_{2}^{2} = 1 - T_{1} T_{2}^{2} = \frac{\sqrt{2} - 1}{2 \sqrt{2}} T_{2}^{2} = \frac{\sqrt{4} - \sqrt{2}}{4} = \frac{\sqrt{a} - \sqrt{b}}{4} a + b = 4 + 2 = 6$

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