If we calculate the difference between one number and the next we get: 9 17 25 33 41 ... Now the difference between each of these differences is 8, suggesting a fixed pattern involving 8. We can call the first term in the series a0=5, the next a1 and so on until a(n). We can see that the differences are related to 8 by position: 1+0*8=1; 1+1*8=9; 1+2*8=17; 1+3*8=25; 1+4*8=33, etc. so for the nth term 1+8n gives us the difference from the first term, which is 5. The series becomes 5, 5+8*1+1, 5+8*1+1+8*2+1, 5+8*1+1+8*2+1+8*3+1, ... We should now be able to work out the nth term. We start with 5 and add n to account for the progression of 1's. Then we have another arithmetic progression multiplied by 8: 8(1+2+3+4...n). The sum to n terms of the natural numbers is n(n+1)/2 so multiplying by 8 we get 4n(n+1). Therefore the expression for the nth term is 5+n+4n(n+1). Let's try it for n=5 and we get 130, which matches the given sequence. The expression can be simplified: 5+n(1+4n+4)=5+n(4n+5). When n=0, the term is 5; when n=1 it's 14. When n=7 the term is 236.