Question

If the 2nd term of a GM series is 25. and the
fifth term is 3125. the first and third terms
are​

Answer 1

Answer:

5, 125

Step-by-step explanation:

$term = a \times {r}^{n - 1}$

$25 = a \times {r}^{2 - 1} \\ 25 = a \times r$

$3125 = a \times {r}^{5 - 1} \\ 3125 = a \times {r}^{4}$

Solving simultaneously:

$a = \frac{25}{r} \: and \: a = \frac{3125}{ {r}^{4} } \\ \frac{25}{r} = \frac{3125}{ {r}^{4} } \\ \frac{ {r}^{4} }{r} = \frac{3125}{25} \\ {r}^{3} = 125 \\ r = 5$

$a = \frac{25}{r} = \frac{25}{5} = 5$

$3rd \: term = 5 \times {5}^{3 - 1} = 5 \times 25 = 125$