What is the distance from (−2, 4) to (0, −6)? Round your answer to the nearest hundredth. 9.23 10.20 10.98 11.34
1 answer:
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Answer:
a) 10th term is 0.051
b) The sum of first 18 terms of given sequence is 51.48
Step-by-step explanation:
We are given the sequence 26, 13, 6.5, ..... we need to find
a) 10th term
b) Sum of first 18 terms
Before solving we need to determine if the sequence is arithmetic or geometric
The sequence is arithmetic if common difference d is same.
The sequence is geometric if common ratio r is same.
Finding common difference d: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5
As common ratio is same so, the sequence is geometric.
a) Finding common difference: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
a) 10th term
The formula to find 10th term is:
We have a₁=26 and r = 0.5 n=10
So, 10th term is 0.051
b) Sum of first 18 terms
The formula to find sum of geometric series is:
where a= 1st term, r = common ratio and n= number of terms
In the given sequence we have
a=26, r=0.5 and n=18
Finding sum of first 18 terms
So, sum of first 18 terms of given sequence is 51.48
You can see that each time x increases by 1, y increases by 5. This means that the coefficient of x is 5 (if you graphed it, the slope would be 5). To find what value to add at the end, you can look at what y is when x equals 0. In this case, that is -2 (on a graph, -2 would be the y-intercept).