Question

7²ⁿ⁺¹ +7²ⁿ⁻¹
---------------- =
100 * 7ⁿ⁻¹

Answer 1

$\frac{ {7}^{2y - 1} (49 + 1)}{100 \times {7}^{y - 1} } = \frac{ {7}^{y} }{2}$

Answer 2

$\displaystyle \tt  \frac{7^{2n+1}+7^{2n-1}}{100\cdot7^{n-1}}=\frac{7\cdot7^{2n}+\dfrac{7^{2n}}{7}}{\dfrac{100\cdot7^{n}}{7}}=\frac{49\cdot7^{2n}+7^{2n}}{100\cdot7^{n}} =\frac{50\cdot(7^{n})^{2}}{100\cdot7^{n}}=\frac{7^{n}}{2};$