Question

If the third term of a GP is 5/2 and its eighth term is 5/64, then find the first term and common ratio

Answer 1

Answer:

First term, a = 10

Common ratio, r = 1/2

Step-by-step explanation:

We are given that the third term of a GP is 5/2 and its eighth term is 5/64.

Let First term of GP be a and common ratio be r.

The formula for nth term of G.P. , $a_n = ar^{n-1}$

So, Third term of GP, $a_3 = ar^{3-1}$

          $ar^{2}$ = 5/2 -------------- [Equation 1]

Eight term of GP, $a_8 = ar^{8-1}$

           $ar^{7}$ = 5/64 -------------- [Equation 2]

Divide equation 1 and 2, we get;

             $\frac{ar^{7} }{ar^{2} } = \frac{5}{64} *\frac{2}{5}$

               $r^{5} = \frac{1}{32}$

               $r^{5} = (\frac{1}{2})^{5}$

Therefore, r = 1/2 and putting r in equation 1 we get, a = (5/2) * 4 = 10 .

So, First term = 10 and common ratio = 1/2.