It is not clear from the question if it is n2 or n^2. I am assuming it is n^2.

Bronze series: first 5 terms

• n2 + 1: take n = 1, we get 2. Similarly for n= 2,3,4,5; we get 5,10,17,26.
• Similarly, for n2+3, we can substitute n as 1,2,3,4,5 and obtain the series as 4,7,12,19,28.

others in the bronze series can be solved similarly.

Silver series: 

• 2n2 + 5: we can substitute n as 1,2,3,4,5; and obtain 7,13,23,37,55. 
• 2n2+7: we can similarly substitute n= 1,2,3,4,5 and obtain the series as 9,15,25,39,57. 

The rest of the series can be similarly solved.

Finding the n the term in series:

3,6,11,18,27: each number is separated by 2 and if we look carefully this is a series of n2+2.

Similarly, next series is n2+6.

Other parts can also be solved similarly.

Hope this helps.