The common ratio of the geometric sequence is 2
What is a series?
The term series has to do with an addition of figures. We can see that the series is give as 5 + 18 + 31 + 44 + ... 161. The sum of the series can be obtained by the use of the formula;
Sn = n/2(a + l)
n = number of terms
a = first term
l = last term
Then;
Un = a + (n - 1) d
161 = 5 + (n - 1)13
161 = 5 + 13n - 13
161 -(5 +13) = 13n
143 = 13n
n = 11
Thus;
Sn = 11/2( 5 + 161)
Sn = 913
The sum of the arithmetic progression is 913.
Again
T11 = ar^10
T6 = ar^5
T11 = T6 + 32
ar^10 = ar^5 + 32
ar^10 - ar^5 = 32
ar^10/ar^5 = 32
r^5 = 32
r = 2
Hence, the common ratio is 2.
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