The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.

fasanya adeola

13 years ago

T=ar^1-1=2r.

=ar^0=2r.

Law of indices.

X^0=1.

: r^0=1.

a=2r.



S=a/1-r

S=8, a=2r.



8=2r/1-r

Cross multiply

8(1-r)=2r

8-8r=2r

8=2r+8r

8=10r

r=4/5.



substitute r=4/5 into a= 2r.



a=2(4/5).

a=8/5.



S=a(1-r^n-1)/1-r that is d sum of G.P.

a=8/5, n=2, r=4/5.



S=[8/5(1-(4/5)^2]/1-r.

=8/5(1-16/25)/1-4/5.

=(8/5x9/25)/1/5

=72/25.

Andyjnr

7 years ago

I don't understand the solution

damilarey1

12 years ago

72/25

ScottEmmy

4 years ago

Is wrong

Ekeeblinks

13 years ago

It can equally b D...cos we werent tld if r> or <1

Lord seyad

13 years ago

The answer is correct,since r=4/5. so it is <1

fmbuzzy

10 years ago

d ansa is 72/25

mynameisesther

2 years ago

the answer is correct
firstly remember the first term is 2 times the common difference
so a=2r
and the sun to infinity is 8
formula for sum to infinity is
S=2r/1-r
8=2r/1-r
cross multiply
8(1-r)=2r
8-8r=2r
collect like terms
8=2r+8r
8=10r
divide both side by 10 to leave r alone
r=8/10 = 4/5
remember a=2r
so a=2(4/5)
a=8/5

so now you can solv for the sun of the first two terms using the formula= a(1-r) / 1-r
since r is less than 1

Johnny1020

3 months ago

the sum of GP is a(1-r^n)/1-r actually