Math Arithmetic Series. ?

Question

In exercises 1-5, find the sum of the arithmetic sequence having the data given.

1.

a1 = 5, an = 3, n = 20

2.

a1 = 7, d = - 3, n = 20

3.

a1 = 81, an = - 13, n = 20

4.

a1 = 5, d = 7, n = 120

5.

an = 5, d = -2, n = 12

In exercises 6-7, find the first term of the arithmetic sequence having the data given.

6. an = 48, Sn = 546, n = 26

7. Sn = 781, d = 3, n = 22

8. The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.

9. How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762?

Thank you plenty.

Answer 1

you should be able to show that the sum of an arithmetic series of n terms is given by "n a_k + {n-1} d ", where a_k is 1st known term &"d" is the common difference found from  [ a _ p - a _w] / [ p - w ]...{ in #3 a_20 - a_1 = -94  so d = -94 / 19  and k = 1....20* 81 + 19*[-94/19] }