Question

The sum of the first 20 terms of an arithmetic series is identical to the sum of the first 22 terms. If the common difference is -2, find the first term.

Answer 1

I bet the the series near zero does this...3, 1,-1, -3

Now use your sum series to find the first term if the twentth term is 3.

Answer 2

sum of 20 = 10(2a + 19d)
= 10(2a - 38)
= 20a - 380
sum of 22 = 11(2a + 21d)
= 11(2a - 42)
22a - 462

22a - 462 = 20a - 380
2a = 82
a = 41

first term is 41

Answer 3

There are n arithmetic means between 1 and 31 such that seventh mean :( n -1)th mean = 5 : 9. Find n.