Question

In a geometrical progression, the sum of the first two terms is 3, and the sum of the second
and third terms is --6. Find the first term and the common ratio.​

Answer 1

Answer:

1st term (a) = 1

Common ratio (r) = 2

Step-by-step explanation:

We know that,

In a G.P,

T1 = a

T2 = ar

T3 = ar²

Now, according to the Question,

T1 + T2 = 3

a + ar = 3

a(1 + r) = 3

(1 + r) = 3/a ------ 1

Again,

T2 + T3 = 6

ar + ar² = 6

ar(1 + r) = 6

But from eq.1 we get,

ar(1 + r) = 6

ar(3/a) = 6

3r = 6

r = 6/3

r = 2

Then, Putting r = 2 in eq.1, we get,

(1 + 2) = 3/a

3 = 3/a

3a = 3

a = 3/3

a = 1

Hence,

1st term = 1

Common ratio = 2

Hope it helped and believing you understood it. All the best.