Question

Find a G.P. for which sum of the first two terms is and the fifth term is 4 times the third term.​

Answer 1

Answer:

GP = 4, -8, 16...

Step-by-step explanation:

Let a be the first term and r be the common ratio of the G.P.

First two terms sum = -4

a + ar = -4    ----- (1)

fifth term is 4 times the third term.

t₅ = 4t₃

=> ar⁴ = 4 * ar²

=> ar⁴ - ar² = 0

=> r²- 4 = 0

=> r = ±2

Place r = 2 in (1), we will get

a + 2a = -4

=> a = -4/3

∴ GP = -4/3, -8/3, -16/3....

Place r = 2 in (1), we will get

=> a - 2a = -4

=> a = 4

Then,

GP is 4, -8, 16...

#MarkAsBrainliest

Answer 2

Step-by-step explanation:

for which sum of first two terms is –4 and fifth term is 4 times the 3rd term. Putting r = 2 in (i), we get a + 2a = -4 a = -4/3. Now, putting r = -2 in (i), we get a + a(-2) = -4 -a = -4 or a = 4. ∴ G.P. is 4, 4(-2), 4(-2)2, .... or 4, -8, 16, ........