Question

find the GP if t3:t4=1:6 and t5=1296​

Answer 1

t3 = ar^2

t4 = ar^3

t5 = ar^4 = 1296

ar^2:ar^3 = 1:6

1:r = 1:6

r = 6

it's is given that ar^4 = 1296

put the value of r

then a(6)^4 = 1296

a = 1

Then gp = a, ar, ar^2, ar^3....

hence

= 1, 6, 36, 216...

hope this one helps you

Answer 2

Answer:

1, 6, 36, 216, 1296, ...

Step-by-step explanation:

As you may know k-th term of a GP is given as --  a*r^(k-1)

where, a is the first term of GP and r is the common ratio of GP

Following from the ques, t3:t4 = a*r^2 : a*r^3 = 1:r = 1:6

so r=6

and t5 = a*r^4 = a*(6^4) = a*1296 = 1296

so, a=1

Hence, GP is:  a, a*r, a*r^2, a*r^3, ....

                     = 1, 6, 36, 216, 1296, ...

hope this helps!!  :)