Question

The 6th through the 9th terms of a geometric sequence are ag = 48, a7 = 96, ag = 192, and ag = 384. What is the value of the first term of this sequence? A 3 4 3 B. C. 1 D. 3 E. 8

Answer 1

Step 1: Write out the terms in the question

`\begin{gathered} a_6=48 \\ a_7=96 \\ a_8=192 \\ a_9=384 \end{gathered}`

Step 2: Find the common ratio ( r )

The ratio between two consecutive terms gives the common ratio

That is,

`r=(a_7)/(a_6)=(a_8)/(a_7)=(a_9)/(a_8)`
`r=(96)/(48)=2`

Step 3: Find the first term by substituting the value of r

Firstly, write out the general term of a geometric progression

`\begin{gathered} a_n=a_1\text{ }* r^(n-1) \\ \text{Thus,} \\ a_6=a_1r^5=48 \\ a_{1\text{ }}\text{ is the first term} \end{gathered}`
`\begin{gathered} \text{IF a}_1* r^5=48 \\ a_1*2^5=48 \\ a_1*32=48 \\ a_1=(48)/(32)=(3)/(2) \end{gathered}`

Thus, the first term is 3/2