Question

If yje ifrst term and fifth term in gp is 16 and 81 find the 4th term

Answer 1

Answer:

4th term = 54

Step-by-step explanation:

first term = a1 = 16

5th term = a4 = 81

common ratio = r

$\frac{a5}{a1} = \frac{a {r}^{4} }{a} = \frac{81}{16} \\ {r}^{4} = \frac{81}{16} \\ r = \sqrt[4]{ \frac{81}{16} } \\ r = \frac{3}{2} \\ \\ {4}^{th} term = a {r}^{3} \\ = 16 \times {( \frac{3}{2} )}^{3} \\ = 16 \times \frac{27}{8} \\ = 2\times 27 \\ = 54$

therefore the 4th term = 54

hope you get your answer