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likoan [24]
3 years ago
7

Jake was 4 times as old as Kelly 5 years ago. Their total age is 60 now. How much older is Jake than Kelly?​

Mathematics
1 answer:
tatyana61 [14]3 years ago
8 0

Answer:

5 years ago

Let Kelly's age be x

Jake's age is 4x

5 years later

Kelly's age is x + 5

Jake's age is 4x+5

The sum of both their ages is 60. The equation will be

x + 5 + 4x + 5 = 60

5x + 10 = 60

5x = 60 - 10

x = 50/5 = 10

So Kelly is (10 + 5) 15 years old.

Jake is (4*10 + 5) = 45 years old

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Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms
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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: a_n=a_1r^{n-1}

We have a₁=26 and r = 0.5 n=10

a_n=a_1r^{n-1}\\a_{10}=26(0.5)^{10-1}\\a_{10}=26(0.5)^{9}\\a_{10}=0.051

So, 10th term is 0.051

b) Sum of first 18 terms

The formula to find sum of geometric series is: S_n=\frac{a(1-r^n)}{1-r}

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

S_n=\frac{a(1-r^n)}{1-r}\\S_{18}=\frac{26(1-(0.5)^{18}}{1-0.5}\\S_{18}=\frac{26(0.99)}{0.5}\\S_{18}=\frac{25.74}{0.5}\\S_{18}=51.48

So, sum of first 18 terms of given sequence is 51.48

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