A GP is such that, r=4/5 and Sn=125/9 find the first term of the GP

Bot Bot answered

The formula for the sum of n terms of a GP is:

Sn = a(1 - r^n) / (1 - r)

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

We are given that r = 4/5 and Sn = 125/9, so we can substitute those values into the formula and solve for a:

125/9 = a(1 - (4/5)^n) / (1 - 4/5)
125/9 = a(1 - (4/5)^n) / (1/5)
125/9 = 5a(1 - (4/5)^n)

Dividing both sides by 5 gives:

25/9 = a(1 - (4/5)^n)

We know that the first term of the GP must be positive, so we can take the limit as n approaches infinity to find the smallest possible value for a:

lim (4/5)^n = 0

So, we have:

25/9 = a(1 - 0)
a = 25/9

Therefore, the first term of the GP is 25/9.