Question

If for a sequence, $t_{n}=\frac{2^{n-2}}{5^{n-3}}$ show that the sequence is a G.P. Find its first term and the common ratio.

Answer 1

❤put this formula=an=n/2(n-1)*d

Answer 2

Answer:

First term is 25/2 and the common ratio 5/2

Step-by-step explanation:

Since we have $t_{n}=\frac{2^{n-2}}{5^{n-3}}.......(1)$

for finding the first term put n =1 in equation (1) we get

$t_{1}=\dfrac{2^{1-2}}{5^{1-3}} = \dfrac{25}{2}$

put n =2 in equation (1) we get

$t_{2}=\dfrac{2^{2-2}}{5^{2-3}} = 5$

First term = 25/2

Common ratio  is  the ratio of second term to the first term.It is represented by r.

$r = \dfrac{\dfrac{5}{1} }{\dfrac{25}{2} } =\dfrac 25$

First term is 25/2 and the common ratio 5/2