If the sum of the series $2+5+8+11.....$ is $60100$, then the number of terms are
- $100$
- $200$
- $250$
- $300$
Reveal answer
Fill a bubble to check yourself
B
Correct answer
Explanation
This is an arithmetic series with a=2, d=3. Sum = n/2 * (2a + (n-1)d). 60100 = n/2 * (4 + (n-1)3) = n/2 * (3n + 1). 120200 = 3n^2 + n. 3n^2 + n - 120200 = 0. Using the quadratic formula, n = (-1 + sqrt(1 + 4*3*120200)) / 6 = (-1 + sqrt(1442401)) / 6 = (-1 + 1201) / 6 = 200.
AI explanation
We treat the given series as an arithmetic progression with the first term a equal to 2 and the common difference d equal to 3. Using the sum formula S = (n/2) * [2a + (n - 1)d], we substitute the values to get 60100 = (n/2) * [4 + (n - 1)3], which simplifies to 120200 = 3n^2 + n. Solving the quadratic equation 3n^2 + n - 120200 = 0 yields n = 200 or a negative value. The result is 200.