The third and sixth terms of a geometric progression(G.P) are 1/4 & 1/32 respectively. Find 1. The first term

Question

2.the common ratio
3. The seventh term

Answer 1

I don't understand it

Answer 2

What's not to understand? They tell you that
ar^2 = 1/4
ar^5 = 1/32
divide, and you have ar^5/ar^2 = r^3 = (1/32) / (1/4) = 1/8
so, r = 1/2
ar^2 = a(1/4) = 1/4, so a = 1
Now, the 7th term is the 6th term times the ratio (ar^6 = ar^5 * r)
= 1/32 * 1/2 = 1/64

Answer 3

A Gp has 6 terms.if the 3rd and 4th terms are 28 and -56 respectively.find
a)the first term
b)the sum of Gp

Answer 4

T3=ar^2= 28
T4=ar^3= -56
r= -56/28; r=-2

From T3=ar^2 =28
T3=a(-2)^2= 28
4a=28
a=7
a=7, r=-2
The sum of a G.P
Sn =a(1-r^n)/1-r
Sn=7[(1-(-2)^n]/1-(-2)
Sn=7(1+2)^n/1+2
Sn=7(3)^n/3
Sn=21^n/3
Sn=7^n.

Answer 5

43

Answer 6

The 4th and 6th terms of a G.P are 1/10 and 1/160 respectively determine the common ratio and the first term