Question

insert 3 numbers between 1 and 256 so that the resulting sequence in geometrical progression

Answer 1

First term is 1
you need to I insert 3 terms in between
so 256 becomes the 5th term
and the answer is as follows

Answer 2

Dear Student,

● Answer -

4, 16 and 64

◆ Explanation -

If we insert 3 terms between 1 and 256, it will be GP with 1 being t1 and 257 being 256.

t1 = a = 1

t2 = ar

t3 = ar^2

t4 = ar^3

t5 = ar^4 = 256

Dividing t5 by t1,

ar^4 / a = 256 / 1

r^4 = 256

r = 4

Now,

t2 = ar = 1×4 = 4

t3 = ar^2 = 1×4^2 = 16

t4 = ar^3 = 1×4^3 = 64

So, three numbers to be inserted are 4, 16 and 64.

Hope this helps you...