# For Sn = 3^(2n - 1) + b; Find the Quotient a9 / a7

**Problem**

The sum of the first *n* terms of a series is 3^(2*n* - 1) + *b*. What is the quotient of the 9^{th} and the 7^{th} term?

A. 81 | C. 83 |

B. 82 | D. 84 |

**Answer Key**

[ A ]

**Solution**

Sum of the first

$S_n = 3^{2n - 1} + b$

*n*terms$S_n = 3^{2n - 1} + b$

*n*^{th} term

$a_n = S_n - S_{n - 1}$

$a_9 = S_9 - S_8$

$a_9 = (3^{17} + b) - (3^{15} + b)$

$a_9 = 114,791,256$

$a_7 = S_7 - S_6$

$a_7 = (3^{13} + b) - (3^{11} + b)$

$a_7 = 1,417,176$

$\text{Quotient} = \dfrac{a_9}{a_7} = \dfrac{114,791,256}{1,417,176}$

$\text{Quotient} = 81$ ← Answer: [ A ]

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