Multiple choice

Find the number of terms in the series 20, $\displaystyle 19\frac{1}{3},$ $18\frac{2}{3}$ ........ of which the sum is 300 ?

  1. 25

  2. 36

  3. 49

  4. both 25 and 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is an arithmetic progression with a = 20 and d = -2/3. Using the sum formula S = (n/2)(2a + (n-1)d) = 300, we get a quadratic equation 300 = (n/2)(40 - (2/3)(n-1)). Solving this yields n = 25 and n = 36.

AI explanation

The series is an arithmetic progression with first term 20 and common difference -1/3. Using the sum formula S = n/2 times (2a + (n-1)d), we substitute the values to get 300 = n/2 times (40 + (n-1)(-1/3)). Simplifying this leads to the quadratic equation n squared minus 121n plus 1800 equals 0. Factoring this gives (n minus 25) times (n minus 36) equals 0, meaning both 25 and 36 are valid answers.

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