Question

If the first term of a G.P. exceeds the second term by 2 and the sum of infinity is 50.

Find the first term and the common ratio.

Answer 1

a = -10

r = 4/5

Explanation:

geometric progression

formula

nth term = ar^n

a1 -a2 = 2

a(1-r)= 2

(1-r) = 2/a

sum of infinity ratio

a/(1-r) = 50

a = 50(1-r)

replace the value of (1-r) with 2/a

a = 50(2/a)

a = 100/a

a^2 = 100

a =
`√(100)`

a = ± 10

finding r

a(1-r)= 2

10(1-r) = 2

1-r = 2/10

1 - r = 1/5

1 + 1/5 = r

r = 4/5

making the sequence

10*4/5 = 8

10 , 8 , 32/5......

since it states that the second term exceeds by two... this means that the second term has to be greater than the first

Hence:

a = -10

meaning the sequence becomes:

-10 , -8 , -32/5

a = -10

r = 4/5