'The length of a rectangle is 6 feet more than three

Mathematics

1 answer:

olga_2 [115]3 years ago

3 0

Answer:

length : 15 ft

width : 3 ft

Step-by-step explanation:

perimeter = 2×l(ength) + 2×w(idth) = 36

l = 3w + 6

=> 2×(3w+6) + 2w = 36

6w + 12 + 2w = 36

8w = 24

w = 3

=> l = 3w + 6 = 3×3 + 6 = 9+6=15

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Let a4+a8+a12+a16=224. Find the sum of first 19 term in sequence.

Tomtit [17]

Without knowing anything about the sequence, this is impossible to answer. But suppose the sequence is arithmetic, in which case each term differs by some constant $k$ :

$a_2=a_1+k$

$a_3=a_2+k=a_1+2k$

$a_4=a_3+k=a_1+3k$

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$a_n=a_{n-1}+k=a_1+(n-1)k$

Then we can write

$a_4+a_8+a_{12}+a_{16}=4a_1+36k=224\implies a_1+9k=56$

and from the formula above, we see this means the 10th term in the sequence is $a_{10}=56$ . But that's all the specific info we can gather about such an arithmetic sequence. If we set the first term to be some unknown $a_1=a$ , then the sum of the first 19 terms in the sequence would be

$\displaystyle\sum_{n=1}^{19}a_n=\sum_{n=1}^{19}\big(a+(n-1)k\big)=19a+k\sum_{n=1}^{18}n=19a+171k$

If we knew one more term in the sequence, we could determine the value of $k$ and derive the value of $a$ (if the first term $a_1$ is not immediately given), and then go on to find an exact numeric value for the sum.