The common difference of this series is 0.1n, because the differences are 0.1, 0.2, 0.3, 0.4.
a1=a0+0.1, a2=a1+0.2, a3=a2+0.3,..., a(n)=a(n-1)+0.1n.
If we subtract 1.5 from each term, we get: 0, 0.1, 0.3, 0.6, 1.0. This is 0, 0+0.1, 0+0.1+0.2, 0+0.1+0.2+0.3, 0+0.1+0.2+0.3+0.4. This is the same as adding up the numbers: 0, 0+1, 0+1+2, 0+1+2+3, 0+1+2+3+4, then multiplying by 0.1. We have a series for adding up all the integers up to n. In this series, if we add the first and last numbers (0+n) we get n, then we add the second and penultimate 1+(n-1) and we get n again, and so on. There are n/2 pairs of these when n is even plus the middle number, which is n/2, so the sum is n/2*n+n/2=n(n+1)/2. If n is odd, we have n(n+1)/2, which is the same formula. So in our series we have 1.5+0.1n(n+1)/2. When n=0, we have the first term, 1.5. When n=4, we have 1.5+1.0=2.5. If we want the count from n=1, so that a1=1.5, then the formula is 1.5+0.1n(n-1)/2. Using this formula, counting from 1, a5=1.5+1.0=2.5.