# Lesson Worksheet: Arithmetic Series Mathematics

In this worksheet, we will practice calculating the sum of the terms in an arithmetic sequence with a definite number of terms.

**Q9: **

Find the arithmetic sequence given the sum starting from the second term is 567, the sum excluding the last term is 469 and the difference between the tenth and sixth terms is 28.

- A
- B
- C
- D
- E

**Q10: **

Find the arithmetic sequence that starts at given that the sum of the first 17 terms is 748 and the arithmetic mean between and is 48.

- A
- B
- C
- D
- E

**Q11: **

Find all possible arithmetic sequences that satisfy and where is the sum of the first terms of the arithmetic sequence, is the term, and is the first term.

- A or
- B or
- C or
- D or

**Q12: **

In an arithmetic sequence that starts at , and the sum of the eighth and the twelfth terms exceeds the fifteenth by 7. Find the number of terms whose sum is 322.

**Q13: **

Find the sum of a sequence which has 9 terms, given that the sum of the first third of the terms is 102 and that of the last third of the terms is . Then, find the sum of the middle five terms.

- A
- B
- C
- D
- E

**Q14: **

The term of an arithmetic sequence is and the first term is .

Find the sum of the positive terms of the arithmetic sequence in which and .

**Q15: **

Find all possible values of for which the sum of the sequence is 264.

- A7 or 12
- B11 or 6
- C8 or 13
- D10 or 5
- E9 or 4

**Q16: **

The term of an arithmetic sequence is and the first term is .

Find the sum of all the terms from to for the arithmetic sequence that starts .

**Q17: **

You open a book to the middle and see page numbers 12 and 13. What is the sum of all the page numbers in the book?

**Q18: **

Find given that the sum of the first terms of the arithmetic sequence is 21 times greater than the sum of the first terms of the arithmetic sequence .

**Q19: **

Find the sum of the first 16 terms of the sequence

**Q20: **

The term of an arithmetic sequence is and the first term is .

Find given that the sum of the first terms of the arithmetic sequence is .

**Q21: **

Find the sum of the sequence of natural numbers which are greater than 64, less than 74, and divisible by 3.

**Q22: **

The term of an arithmetic sequence is , the first term is , and the sum of the first terms is .

Find given that .

**Q23: **

Anthony inserts 5 arithmetic means between and . Benjamin inserts 3 arithmetic means between the same numbers, and . If the sum of Anthony's 5 means exceeds that of Benjamin's 3 means by 112 and the first mean of the Anthony exceeds the first mean of Benjamin by 2, find the value of and .

- A,
- B,
- C,
- D,
- E,

**Q24: **

Find the sum of the first 35 terms in the sequence .