Question

What’s the answer to this?

Answer 1

Answer:

The missing term is:

$a_2=14$

Step-by-step explanation:

Considering the geometric sequence

$2,\:?,\:98,\:...$

Here,

$a_1=2$

$a_3=98$

$a_2=?$

The general term of a geometric sequence is given by the formula:

$a_n=a_1\cdot \:r^{n-1}$

where $a_1$ is the initial term and $r$ the common ratio.

as

$a_3=a_1\cdot \:r^{3-1}$

$98=2\cdot \:r^{3-1}$         ∵ $a_1=2$

$\mathrm{Switch\:sides}$

$2r^{3-1}=98$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2r^{3-1}}{2}=\frac{98}{2}$

$r^{3-1}=49$

$r^2=49$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$r=\sqrt{49},\:r=-\sqrt{49}$

$r=7,\:r=-7$

Taking positive value of $r = 7$

$a_2=a_1\cdot \:r^{n-1}$

putting $r = 7$

$a_2=2\cdot \:7^{2-1}$

$a_2=2\cdot \:7$

$a_2=14$

So, the sequence becomes  $2,\:14,\:98,\:...$

Therefore, the missing term is:

$a_2=14$