MBA Exam Numerical Ability Arithmetic

Find the sum of 1st 20 terms of the series 1, 6, 21, 52, 105, 186,... . (this ques appeared in AIMCAT but i am nt getting the method used by them. i want a general approach.

1) 28880
2) 28740
3) 41440
4) 47180
5) 42410

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MBA Other Question
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? 40506080None of these

1) 1
2) 2
3) 3
4) 4
5) 5
 let S be a set of 5 digit numbers formed by the digits 1, 2, 3, 4 and 5 using each digit exactly once such that exactly 2 odd positions are occupied by odd digits. what is the sum of the digits in the rightmost position of the numbers of S?please tag me while explaining the answer... thank you..

1) 228
2) 216
3) 294
4) 192