Maths · Arithmetic and Geometric progressions
If the first, second and last terms of an
If the first, second and last terms of an
- A. P be \( a, b, 2 a \) respectively, then its sum will be A \( \cdot \frac{a b}{-a+b} \)
- B. \( \frac{a b}{2(b-a)} \)
- C. \( \frac{3 a b}{2(b-a)} \)
- D. \( \frac{3 a b}{4(b-a)} \)
Step-by-step solution
In an AP, first term = a, second term = b, so common difference d = b - a. Last term = 2a gives number of terms n = 1 + a/(b-a) = b/(b-a). Sum = n/2 * (first + last) = (b/(b-a))/2 * (a+2a) = (b/(b-a)) * (3a/2) = 3ab/(2(b-a)).
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