10 - கணிதம் - அலகு 2.

The given sequence is a Fibonacci sequence, where each term is the sum of the two preceding terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and 8. To find the 8th term, we need to continue the sequence by adding the previous two terms. Therefore, the 8th term is 13.

The given series is a decreasing sequence where each term is obtained by subtracting 1/20 from the previous term. Therefore, to find the next term, we subtract 1/20 from the current term. By doing so, we get 1/30 as the next term in the series.

The correct answer is "ஒரு கூட்டுத்தொடர் வரிசை" because the given sequence follows a pattern where each term is obtained by adding a constant value to the previous term.

The given sequence is formed by adding 7 to each element after multiplying it by 3. This is evident from the pattern of the sequence, where each element is obtained by multiplying the corresponding letter by 3 and adding 7. Therefore, the sequence can be classified as a "கூட்டுத்தொடர்வரிசை" (increasing sequence) where each term is obtained by adding a constant value to the previous term.

The given sequence of fractions is in ascending order. The numerator of each fraction is 1, while the denominators are 3, 5, 1, and 5 respectively. The fraction 1/3 is the first fraction in the sequence, which is the correct answer.

The given expression is a-4b+6c-4l+m. Since there is no information given about the values of a, b, c, l, and m, we cannot determine the exact value of the expression. However, if we assume that a, b, c, l, and m are all equal to zero, then the expression simplifies to 0-0+0-0+0=0. Therefore, the answer is 0.

The given sequence is (2), (1), (4), (3).

The given expression, 100n+10, represents a sequence of numbers where each term is obtained by multiplying n by 100 and then adding 10. This is a linear sequence with a common difference of 100. Therefore, the correct answer is "ஒரு கூட்டுத்தொடர் வரிசை" which translates to "an arithmetic sequence" in English.

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The given expression is a/b, which represents the ratio of a to b. In the given sequence, a/b is the only option that represents the ratio between two elements in the sequence. The other options do not represent any ratio between the given elements. Therefore, a/b is the correct answer.

The given sequence is formed by adding a constant value to each term. The pattern is that each term is obtained by adding (x+1) to the previous term. Therefore, the sequence is an arithmetic sequence with a common difference of (x+1). This type of sequence is known as a "progression" or "பெருக்குத் தொடர்வரிசை" in Tamil.

The given expression 1/(a/c) simplifies to c/a. Therefore, the correct answer is c/a.

In a geometric progression, each term is obtained by multiplying the previous term by a constant factor. In this case, the common ratio is 3/2. Starting with the first term 5, the second term is obtained by multiplying 5 by 3/2, which gives 7.5. Similarly, the third term is obtained by multiplying 7.5 by 3/2, which gives 11.25. Therefore, the first term in the sequence is 5, the second term is 7.5, and the third term is 11.25. So, the correct answer is (1).

The given sequence is repeating the number -3 continuously. This is an example of a periodic sequence where the same number or pattern repeats after a certain interval. In this case, the interval is 1, as the sequence is repeating the number -3 after every term. Therefore, the sequence can be classified as both an arithmetic sequence (as the difference between consecutive terms is 0) and a geometric sequence (as the ratio between consecutive terms is 1).

The given answer is (1) because it states that the additional elements in the n-th term of the sequence are the first n elements of the sequence. This means that the sequence is formed by adding the first n terms to the original sequence.

The given expression consists of three terms: k+2, 4k-6, and 3k-2. We are asked to find the value of k. By comparing the given expression with the answer choices, we can see that the third option, 5, satisfies the expression. When k=5, the three terms become 7, 14, and 13 respectively. Therefore, the value of k is 5.

Each of the given options provides a statement about a sequence or series. Option (1) states that every term determines a sequence. This means that each term in the given series determines a sequence or series. The other options either discuss the calculation or representation of the terms in the series, but do not specifically address the relationship between the terms and a sequence. Therefore, option (1) is the correct answer.

The given question is asking for the correct symbol to fill in the blanks. The equation given is a sum of consecutive numbers from 1 to n. The correct symbol to fill in the blanks is "+". This is because the equation is asking for the sum of all the numbers from 1 to n, and the "+" symbol is used to indicate addition. Therefore, the correct answer is (1).

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The given arithmetic sequence has a common difference of 4 and the third term is being asked. To find the third term, we can use the formula:

nth term = first term + (n-1) * common difference

Plugging in the values, we get:

3rd term = 16 + (3-1) * 4 = 16 + 2 * 4 = 16 + 8 = 24

Therefore, the answer is 24.