Find a GP for which the sum of the first two terms is - 4 and the fifth term is 4 times the third term. Class 9

Find a GP for which the sum of the first two terms is - 4 and the fifth term is 4 times the third term. Class 9

Question 1.

Find a GP for which the sum of the first two terms is - 4 and the fifth term is 4 times the third term. Class 9

Solution:

Sum of first two terms = - 4 ... [Given]

∴ a + ar = - 4

∴ a (1 + r) = -4 ... (i)

Also, fifth term = 4 × third term ... [Given]

∴ ar⁴ = 4 (ar²)

∴ r⁴ = 4r²

r² = 4

∴ r = 2 or - 2

When, r = 2

a(1 + 2) = -4 ... [From (i)]

∴ 3a = -4

a = $-\frac{4}{3}$

∴ The required GP is a, ar, ar²,...

i.e., $-\frac{4}{3},-\frac{8}{3},-\frac{16}{3}, \ldots$

When, r = -2

a (1 - 2) = -4 ... [From (i)]

∴ -a = - 4

∴ a = 4

∴ The required GP is a, ar, ar², ...

i.e., 4, -8, 16,...