What is the sum of the first 7 terms of the series -4 + 8 - 16 + 32 -...?

Solution:

Let S_n = -4 + 8 - 16 + 32 -...

Here, t₂ / t₁ = 8 / (-4) = -2; 

t₃ /  t₂ = (-16) / 8 = -2; 

⇒ t₂ / t₁ = t₃ / t₂ 

∴ The given series is geometric progression.

Sum of ‘n’ terms = S_n = [a (1 - rⁿ)] / (1 - r)

Here, a = 1st term = -4, r = t₂ /  t₁ = -2 and n = 7

S₇ = [(-4) × (1 - (-2)⁷)] / (1 - (-2))

S₇ = [(-4) × (1 + 128)] / 3

S₇ = -172

What is the sum of the first 7 terms of the series -4 + 8 - 16 + 32 -...?

Summary:

The sum of the first 7 terms of the series -4 + 8 - 16 + 32 -... is S₇ = -172.