Arithmetic Sequence And Series Quiz!

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.

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.

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.

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.

The common difference in this arithmetic sequence is -3 (each term is 3 less than the previous one). To find out which term is -29, we can follow these steps:

Find the difference between the first term and -29: -29 - 4 = -33

Divide the difference by the common difference: -33 / -3 = 11

Add 1 to the result (because we started with the first term): 11 + 1 = 12

Therefore, -29 is the 12th term of the sequence.

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. 

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.

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.

To find the 20th term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where:

a_n is the nth term

a_1 is the first term

d is the common difference  

In this sequence, a_1 = 3 and d = 4. Substituting these values and n = 20 into the formula:

a_20 = 3 + (20 - 1) * 4 a_20 = 3 + 19 * 4 a_20 = 3 + 76 a_20 = 79