I need to find out what I am increasing by in this problem. a sub 1 = 15 and a sub 100 = 307 what is the sum of the first 100 terms?

Question

a₁=15 and a₁₀₀ = 307 find the sum of the first 100 terms

Answer 1

It appears that you are dealing with an arithmetic sequence.

 

a₁₀₀ = a₁ + 99d

307 = 15 + 99d

d = 2.949494... which equals 2 94/99 or 292/99, a very unusual constant difference.

 

But you can find the sum of n=100 terms by the formula S_n = (n/2)(a₁ + a_n).