First, you have to transform your numbers into proper fractions: 1 and 3/5 = (5+3)/5 = 8/5 1 and 1/5 = (5+1)/5 = 6/5
Therefore your arithmetic sequence is 2, 8/5, 6/5, ...
In an arithmetic sequence, the difference between a given term and the preceding one is equal to the difference between the <span>following </span>term and the given one. In your case: d = 8/5 - 2 = (8-10)/5 = -2/5 As a prove: d = 6/5 - 8/5 = -2/5
Now, in order to find the 25th term you need to apply the formula: an = a + (n - 1)d where an is the number you are looking for, a is the first term, n is the term you are looking for and d is the distance. Hence, a₂₅ = 2 + (25-1)(-2/5) = 2 - 24·2/5 = 2 - 48/5 = (10-48)/5 = -38/5
