Question

If the 2

nd term of geometric sequence is − and the 5

th term is . Find the first

three terms of gometric sequence.​

Answer 1

`(3)/(2)`, - 3, 6.

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.
`ar^(4) = 24` .......... (2)

Now, dividing equation (2) by equation (1) we get,

`(ar^(4) )/(ar) = (24)/(- 3)`

⇒
`r^(3) = - 8`

⇒ r = - 2

Therefore, from equation (1) we get, a( - 2) = - 3

⇒
`a =(3)/(2)`

Hence, the first three terms of the G.P. are
`(3)/(2)`, - 3, 6. (Answer)