Question

Define the type of sequence below. 7, 14, 28, 56, 122, ...

Answer 1

The sequence is a geometric sequence

Answer 2

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 $a_n.$

Then, we see the following relation between the consecutive terms of the given sequence :

$\dfrac{a_2}{a_1}=\dfrac{14}{7}=2,\\\\\\\dfrac{a_3}{a_2}=\dfrac{28}{14}=2,\\\\\\\dfrac{a_4}{a_3}=\dfrac{56}{28}=2,\\\\\\\dfrac{a_5}{a_4}=\dfrac{122}{56}=2,\\\\\\\vdots~~~~~~\vdots$

Therefore, we get

$\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}=~~.~~.~~.~~=2.$

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.