Chapter 12 Sequences and Series - Standardized Test Practice - Gridded Answer - Page 847: 8

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Given: $a_3=12\\a_5=48$ Since the sequence is geometric, we have: $12=a_3=a_1\times r^2\\45=a_5=a_1\times r^4$ Obtain: $45=a_1 \times r^4\\45=a_1\times r^2 \times r^2\\45=a_3\times r^2\\r^2=\frac{45}{12}=\frac{15}{4}$ Hence, we find $a_1 \times r^2=a_3\\a_1 \times \frac{15}{4}=12\\a_1=\frac{16}{5}$