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The sum of the first 6 terms of a geometric sequence is 39.375 and the common ratio is 0.5 write the geometric sequence series using summation notation

Respuesta :

taskmasters
Given:
n = 6
sum of the first 6 terms = 39.375
common ratio = 0.50

Formula: 
Sn = a1(1-r^n) / 1 - r ; r ≠ 1

39.375 = a1(1 - 0.5^6) / 1 - 0.5
39.375 = a1(0.984375 / 0.5
39.375 * 0.5 = a1(0.984375)
19.6875 = a1(0.984375)
19.6875/0.984375 = a1
20 = a1

a1 = 20
a2 = 20 x 0.5 = 10
a3 = 10 x 0.5 = 5
a4 = 5 x 0.5 = 2.5
a5 = 2.5 x 0.5 = 1.25
a6 = 1.25 x 0.5 = 0.625

20 + 10 + 5 + 2.5 + 1.25 + 0.625 = 39.375

The geometric sequence is: 20, 10, 5, 2.5, 1.25, 0.625....