Series - Mary learned 20 new French wordds on January 1, 24 on January 2,

Question

Mary learned 20 new French wordds on January 1, 24 on January 2, 28 on January 3, and so on, through January 31. How many words has she learned during January.

My solution is 2480. Could someone check if this is right?

Many thanks in advance

Answer 1

That is correct. There are several ways to think about the solution, but one is as follows:

S = 20 + 24 + 28 ... + 140

S = 20 + (20+4) + (20+8) + ... + (20+120)

S = 20 + 4(1 + 2 + 3 ... + 30) + 20*30

S = 20 + 4[30(30+1)/2] + 600

S = 620 + 60(31)

S = 2480