Arithmetic Sequence And Series Quiz!

Explanation
The common difference in an arithmetic sequence is the constant value that is added or subtracted to each term to get the next term. In this case, we can see that each term is obtained by adding 1/4 to the previous term. Therefore, the common difference in this arithmetic sequence is 1/4.

Explanation
The sum of all odd integers between 8 and 26 can be found by adding all the odd numbers in that range. The odd numbers between 8 and 26 are 9, 11, 13, 15, 17, 19, 21, 23, and 25. Adding these numbers together, we get 153.

Explanation
To insert three arithmetic means between 11 and 39, we calculate the sequence's common difference, finding it to be 7. Placing the means creates a sequence where each term increases by 7 from the previous one. The second arithmetic mean, positioned as the third term in this sequence, is calculated as 11 plus twice the common difference (14), resulting in 25, aligning with arithmetic sequence principles.

Explanation
To find the term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term, d is the common difference, and n is the term number. In this case, the first term is 4 and the common difference is -3. Plugging in these values, we get a12 = 4 + (12-1)(-3) = 4 + 11(-3) = 4 - 33 = -29. Therefore, the 12th term of the arithmetic sequence is -29.

Explanation
The common difference of an arithmetic sequence is the constant value added to each term to get the next term. In this case, we can find the common difference by subtracting the 1st term (2) from the 18th term (87). 87 - 2 = 85. Therefore, the common difference of the sequence is 85 divided by the number of terms between the 1st and 18th term, which is 17. 85 / 17 = 5.

Explanation
To find the sum of all the multiples of 3 from 15 to 48, we can use the formula for the sum of an arithmetic series. The first term is 15, the last term is 48, and the common difference is 3. We can calculate the number of terms using the formula (last term - first term) / common difference + 1. In this case, the number of terms is (48 - 15) / 3 + 1 = 12. Then, we can use the formula for the sum of an arithmetic series, which is (number of terms / 2) * (first term + last term). Plugging in the values, we get (12 / 2) * (15 + 48) = 6 * 63 = 378. Therefore, the correct answer is 378.

Explanation
The given sequence starts with 7 and increases by 2 with each term. To find the nth term, we need to determine the pattern. We can see that the first term is obtained by adding 5 to 2 times the position of the term (n). Therefore, the nth term of the sequence can be represented as 2n+5.

Explanation
To form an arithmetic sequence, the difference between consecutive terms must be constant. In this case, the common difference can be found by subtracting the second term from the first term: (5p+12) - (7p+2) = -2p + 10. Similarly, the difference between the third and second term is: (2p-1) - (5p+12) = -3p - 13. Since both differences must be equal, we can set them equal to each other and solve for p: -2p + 10 = -3p - 13. Simplifying this equation, we get p = -23. Therefore, the correct answer is -23.

Explanation
The value of Glenn's car after 4 years can be calculated by multiplying the initial value of Php 60,000 by (1 - 0.10)^4, which represents the yearly depreciation. This calculation results in Php 43,740. Therefore, the correct answer is Php 437,400.

Explanation
Kelly plans to save Php 3,750 per week for 8 weeks. So, to find out how much she will have saved after 8 weeks, we need to multiply Php 3,750 by 8. Php 3,750 multiplied by 8 equals Php 30,000. Adding this to her initial savings of Php 50,000, Kelly will have a total of Php 80,000.