Question

ES 5 o B. Breaking the CODE! For you to break the code, match Column A to Column B. Write the letter before each number. (10 points) А B A. a1 = an + (n - 1) d B. Sn = ? (a1 + an) D. 230 E. Arithmetic sequence 1) 1, 4, 9, 16, 25, ... 2) 4, 8, 12, 16, 20 3) an= n2 + 1 4) 4, 7, 10, ..., 20 5) 5 + 9 + 13 + 17 + ... +41 6) First arithmetic mean between 3 and 15 if we will insert 2 means. 7) 10th term of the sequence 2, 9, 16, 23, ... 8) The terms are obtained by adding a J. Common difference L. Not Arithmetic Sequence N. 65 0.7 U. Common number W. Infinite Sequence constant. CODE.​

Answer 1

Step-by-step explanation:

ES 5 o B. Breaking the CODE! For you to break the code, match Column A to Column B. Write the letter before each number. (10 points) А B A. a1 = an + (n - 1) d B. Sn = ? (a1 + an) D. 230 E. Arithmetic sequence 1) 1, 4, 9, 16, 25, ... 2) 4, 8, 12, 16, 20 3) an= n2 + 1 4) 4, 7, 10, ..., 20 5) 5 + 9 + 13 + 17 + ... +41 6) First arithmetic mean between 3 and 15 if we will insert 2 means. 7) 10th term of the sequence 2, 9, 16, 23, ... 8) The terms are obtained by adding a J. Common difference L. Not Arithmetic Sequence N. 65 0.7 U. Common number W. Infinite Sequence constant. CODE.

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Answer 2

The question is properly mentioned in the pic attached.

The code to be cracked to this question is WELL DONE!

Given:

In the question, we were give two columns and we have to match them with the correct answer.

To Find:

we have to break the code by matching them with the correct choice.

Solution:

We will solve this problem by solving column A and matching them with column B.

in column A the first question is

1) 1,4,9,16,25, ..............

By looking at this we can say that the given terms were the squares of the natural numbers. We can obtain this sequence till infinite terms. So this sequence can be termed as Infinite Sequence. This matches with option W in column B.

The correct match to this question is option W.

2) 4,8,12,16,20

The given sequence is an Arithmetic sequence as the common difference between the terms is 4. The common difference is found by subtracting the two consequent terms.

$d=8-4=4\\d1=12-8=4$

Since the common difference between them is equal. The given sequence is an Arithmetic Sequence.

The correct match to this question is option E.

3) $a(n)=n^{2} +1$

The given question is an expression to obtain the terms of a sequence.

the first term is obtained by substituting the value of 1 in the place of n.

we get $a1=1^{2} +1=2$

In the same manner we will obtain the value of other terms to check if it is an arithmetic sequence or not.

$a2=2^{2} +1=5\\a3=3^{2} +1=10$

calculate the common difference between the terms.  

$d=5-2=3\\d1=10-5=5$

the common difference between them is not equal. Hence the terms are not in an Arithmetic Sequence.

The correct match to this question is option L.

4) 4,7,10,...........,20

Let us check whether this is an Arithmetic Sequence or not.

the common difference is $7-4=10-7=3$. As the common difference is 3, let us find of the terms of the sequence.

the first term would be 4.

the second term would be 4+3=7.

the third term would be 7+3=10.

the remaining terms would be obtained in the same manner.

$4,7,10,13,16,19,22,........$

We didn't find 20 from the arithmetic sequence we obtained.

Hence the given sequence is not an arithmetic sequence.

The correct match to this question is option L.

5) 5+9+13+17+.....+41

In this question they asked us to find the sum of the terms in a sequence.

The given sequence is an arithmetic sequence as the common difference between the terms is same.$9-5=13-9=17-13=4$

The sum of the terms is given by the formula

$s(n)=\frac{n}{2} (a+l)$

where n is the number of terms , a is the first term and l is the last term in the sequence. To use this formula we should know the value of n.

$a(n)=a+(n-1)d$

$41=5+(n-1)4$

$36=(n-1)4\\n-1=9\\n=10$

the number of terms in the sequence is 10.

$s(10)=\frac{10}{2} (5+41)\\ =5(46)\\ =230$

The correct match to this question is option D.

6)First arithmetic mean between 3 and 15 if we insert 2 means.

If we insert two arithmetic means between them the total number of terms becomes 4. The value of n is 4. Let us find the common difference between them.

$a(n)=a+(n-1)d\\15=3+(4-1)d\\15=3+3d\\12=3d\\d=4$

the first arithmetic mean is 3+4=7.

The correct match to tis question is option O.

7) 10th term of the sequence 2,9,16,23,......

The given sequence is an Arithmetic sequence.

The common difference is $n=9-2=7$.

The n th term in the sequence is given by

$a(n)=a+(n-1)d\\a(10)=2+(10-1)7\\a(10)=2+(9)7\\a(10)=2+63\\a(10)=65$

The correct choice to this question is option N.

8)The terms are obtained by adding a constant .

It is the definition of the Arithmetic Sequence. In this sequence each term differs by a constant value, which means each term is obtained by adding a constant value.

The correct match to this question is option E.

Now write all the letters together to break the code WELL DONE!

Therefore the code is WELL DONE!.

#SPJ3