Discussion

If the first term of a G.P. is 5 and the sum of first three terms is 35/4. What is the common ratio?

Answer: C

\[ S_{3} = a(1 + r + r^{2}) = \frac{35}{4} \]

\[ 1 + r + r^{2} = \frac{7}{4} \quad\Longrightarrow\quad 4r^{2} + 4r - 3 = 0 \]

\[ r = \frac{-4 \pm \sqrt{16 + 48}}{8} = \frac{-4 \pm 8}{8} \]

\[ r = \frac{1}{2} \quad\text{or}\quad r = -\frac{3}{2} \]

Both roots are valid common ratios, so both answers apply.

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