Topic: Arithmetic and geometric progressions. 1. The term of the series -2,1,4,7,10 is:
a) 145
b) 295
c) 895
d) 595
2. If in a PA, the first term is -2, the term 200 is 396, then its difference (d) is:
A) 5
B) 2
C) 4
D) 3
3. In a PA the eighth term is 161, d = 2, so the first term is:

A) 3
B) -1
C) 2
D) 4
4. If in a PA, the last term is 289, the first is 13 and the difference d = 4, then the number of “n” terms is:
A) 70
B) 71
C) 69
D) 68
5. In the series: 1,4,7,10,… .the sum of the first 300 terms is:
A) 134850
B) 133950
C) 89850
D) 850
Help me please!!

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.