Question

5 GM between 5 and 320

Answer 1

anss...... mark me brainlist

Answer 2

you mean, we have to find out 5 geometric progression between 5 and 320.

okay Let's start to find out .
let five geometric means are placed between 5 and 320 in such a way that ; 5 , 5r , 5r² , 5r³ , 5r⁴ , 5r⁵, 320 .

now, you can see there are 7 terms in GP where first term is 5 and r is the common ratio.
so, $T_7=ar^{7-1}$
=> 320 = 5r^6
=> 64 = r^6
=> 2^6 = r^6 hence, r = 2

now, first GM = 5r = 5 × 2 = 10
2nd GM = 5r² = 5 × 2² = 20
3rd GM = 5r³ = 5 × 2³ = 40
4th GM = 5r⁴ = 5 × 2⁴ = 80
5th GM = 5r⁵ = 5 × 2⁵ = 160