Answer:
[tex]\frac{3}{2}[/tex], - 3, 6.
Step-by-step explanation:
Let us assume that the geometric sequence is given by
a, ar, ar², ar³, .........
where a is the first term and r is the common ratio.
Now, given that 2nd term of the G.P. is -3 i.e. ar = - 3 ........ (1)
And the 5th term of the G.P. is 24 i.e. [tex]ar^{4} = 24[/tex] .......... (2)
Now, dividing equation (2) by equation (1) we get,
[tex]\frac{ar^{4} }{ar} = \frac{24}{- 3}[/tex]
⇒ [tex]r^{3} = - 8[/tex]
⇒ r = - 2
Therefore, from equation (1) we get, a( - 2) = - 3
⇒ [tex]a =\frac{3}{2}[/tex]
Hence, the first three terms of the G.P. are [tex]\frac{3}{2}[/tex], - 3, 6. (Answer)
