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Blababa [14]
3 years ago
13

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

Mathematics
1 answer:
Tomtit [17]3 years ago
7 0

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

\ldots

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.

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Svetllana [295]

Answer: At 01:05 p.m. it will overlap again.

Explanation:

Since there are 22 times in a day the minute and the hour hands overlap.

During the first half of the day , it overlaps 11 times and during the rest of the day it overlap 11 more times.

At noon, the minute and the hour hands overlap and after that it will happen at 01:05 p.m.

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3 years ago
Using distributive property what is the value of the expression for 2(-5 + 3)
Vladimir [108]

Answer:

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Step-by-step explanation:

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The terms that we have are now -10 and 6. Add them together to get the final answer.

-10+6=-4

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2 years ago
People travel by bus or by train from hiraddug station on tuesday 420 people travelled by bus from the station the ratio of the
goldenfox [79]

The number of people travelled by train from the station on tuesday is 357.

Let us assume the number of people who travelled by train from the station on tuesday be x. Using the concept of ratio and proportion to solve and calculate x.

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Solving the ratio and proportion for the value of x

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Performing multiplication in numerator

x = 7140 ÷ 20

Performing division on Right Hand Side of the equation

x = 357

Therefore, based on the information, 357 people used to travel.

Learn more about ratio and proportion -

brainly.com/question/12024093

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