Question

Write the first four terms of the geometric sequence satisfying the following conditions: a = 2, anda3 = 50

Answer 1

a_2 = 10

1) Since the first term is 2, and the third one is 50 we can find the second term by calculating the Geometric Mean.

2) So we can write out this:

`\begin{gathered} (2,x,50) \\ x=\sqrt[]{50\cdot2} \\ x=\sqrt[]{100} \\ x=10 \end{gathered}`

Note that the 2nd term is the geometric mean of the 1st and 3rd ones. To find that out we take the square root of those two numbers.

3) Hence, the second term is 10. And we can prove it since

10/2 = 5

50/10= 5 The same ratio q = 5