Question

The ratio of 4th to 12th term of a Go, with positive common ratio is 1/256. If the sum of the 2 terms is 61.68. Find the sum of the series to the 8th term

Answer 1

Step-by-step explanation:

Given The ratio of 4th to 12th term of a Go, with positive common ratio is 1/256. If the sum of the 2 terms is 61.68. Find the sum of the series to the 8th term

• We know that n th term of G.P  a, ar,ar^2 is tn = ar^n-1
• Also sum to n terms of a G.P is Sn = a(r^n – 1) / r – 1
• Given t4 / t12 = 1/256
• Or ar^3 / ar^11 = 1/256
• So 1/r^8 = 1/256
• Or r^8 = 256
• Or r^8 = 2^8
• Therefore r = 2
• Now t12 + t4 = 61.68
• So ar^11 + ar^3 = 61.68
• So a(r^11 + r^3) = 61.68
• So a(2^11 + 2^3) = 61.68
• So a(2048 + 8) = 61.68
• So  a = 61.68 / 2056
• Or a = 3/100
• Now sum of 8 terms of G.P will be  
• S8 = a(r^8 – 1) / r – 1
•     = 3/100 (2^8 – 1) / 2 – 1
•     = 3/100 (256 – 1) / 1
•    = 3/100 (255)  
•   = 153 / 20
• Or S8 = 7.65

Reference link will be

https://brainly.in/question/3840818