Question

2,5, 25/2, ... find the 10th term

Answer 1

Answer:

The  $10^{th}$ term of the given sequence

$t_{10} = \frac{5^{9} }{2^{8} }$

Step-by-step explanation:

Step(i):-

Given sequence   2 , 5, $\frac{25}{2}$

First term    a = 2

The difference of given geometric sequence

    $d = \frac{r_{2} }{r_{1} } = \frac{5}{2}$

Step(ii):-

The  $n^{th}$ term of the given sequence

$t_{n} = ar^{n-1}$

The  $10^{th}$ term of the given sequence

$t_{10} = (2)(\frac{5}{2} )^{10-1}$

$t_{10} = (2)(\frac{5}{2} )^{9}= \frac{5^{9} }{2^{8} }$