Find the sum of the following geometric progressions : 4, 2, 1, 1/2 �

1.	Find the sum of the following geometric progressions : 4, 2, 1, 1/2 ….. to 10 terms.
Answer» Common Ratio = r = \(\frac{2}{4} = \frac{1}{2}\) ∴ Sum of GP for n terms = \(\frac{a(r^n-1)}{r-1}\) ....... (1) ⇒ a = 4, r = \(\frac{1}{2}\), n = 10 ∴ Substituting the above values in (1) we get, ⇒ \(\cfrac{\big(4(\frac{1}{2})^8 - 1\big)}{\frac{1}{2} - 1}\) ⇒ \(\frac{-4 \times 255 \times 2}{-1 \times 256}\) ⇒ \(\frac{255}{32}\)

Find the sum of the following geometric progressions : 4, 2, 1, 1/2 ….. to 10 terms.

Answer»

Common Ratio = r = \(\frac{2}{4} = \frac{1}{2}\)

∴ Sum of GP for n terms = \(\frac{a(r^n-1)}{r-1}\) ....... (1)

⇒ a = 4, r = \(\frac{1}{2}\), n = 10

∴ Substituting the above values in (1) we get,

⇒ \(\cfrac{\big(4(\frac{1}{2})^8 - 1\big)}{\frac{1}{2} - 1}\)

⇒ \(\frac{-4 \times 255 \times 2}{-1 \times 256}\)

⇒ \(\frac{255}{32}\)