Answer: The given sequence is a GEOMETRIC sequence with first term 7 and common ratio 2.
Step-by-step explanation: We are given to define the type of the following sequence :
7, 14, 28, 56, 122, . . .
Let us denote the n-th ter of the given sequence by [tex]a_n.[/tex]
Then, we see the following relation between the consecutive terms of the given sequence :
[tex]\dfrac{a_2}{a_1}=\dfrac{14}{7}=2,\\\\\\\dfrac{a_3}{a_2}=\dfrac{28}{14}=2,\\\\\\\dfrac{a_4}{a_3}=\dfrac{56}{28}=2,\\\\\\\dfrac{a_5}{a_4}=\dfrac{122}{56}=2,\\\\\\\vdots~~~~~~\vdots[/tex]
Therefore, we get
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}=~~.~~.~~.~~=2.[/tex]
That is, there is a common ratio of 2 between any two consecutive terms of the sequence.
Thus, the given sequence is a GEOMETRIC sequence with first term 7 and common ratio 2.
