Consider the arithmetic series 3/2+2+5/2
Calculate the least number of terms that can be added,if the answer must be less than 300
The arithmetic series is 3/2, 2, 5/2.
To find the common difference, we can subtract the first term from the second term: 2 - 3/2 = 4/2 - 3/2 = 1/2.
Since we are looking for the least number of terms that can be added to the series, we want to find the largest term that is less than 300.
The nth term of an arithmetic series is given by the formula: a + (n-1)d, where a is the first term and d is the common difference.
Let's consider the nth term to be less than 300: a + (n-1)d < 300
Substituting the values from the given series, we have: 3/2 + (n-1) * 1/2 < 300
Simplifying the inequality: 3/2 + (n-1)/2 < 300
Multiplying by 2 to get rid of the fraction: 3 + n - 1 < 600
Combining like terms: n + 2 < 600
Subtracting 2 from both sides: n < 598
Since n must be a whole number, the least number of terms that can be added is 597.