Answer:
31/2 or 15½
Explanation:
From the question given above, the following data were obtained:
First term (a) = ½
9th term (T₉) = 128
Sum of 5th term (S₅) =?
Next, we shall determine determine the common ratio of the sequence. This can be obtained as follow:
First term (a) = ½
9th term (T₉) = 128
Common ratio (r) =?
T₉ = ar⁸
128 = ½ × r⁸
Cross multiply
r⁸ = 128 × 2
r⁸ = 256
Express 256 in index form with 2 as the base
r⁸ = 2⁸
r = 2
Finally, we shall determine the sum of the 5th term. This can be obtained as follow:
First term (a) = ½
Common ratio (r) =
Number of term (n) = 5
Sum of 5th term (S₅) =?
Sₙ = a[rⁿ – 1] / r – 1
S₅ = ½[2⁵ – 1] / 2 – 1
S₅ = ½[32 – 1] / 1
S₅ = ½ × 31
S₅ = 31/2 or 15½
Thus, the sum of the 5th term of the sequence is 31/2 or 15½