Maths · Arithmetic and Geometric progressions
The number of terms of an is even; the sum of the odd terms is and of the even t
The number of terms of an \( A . P . \) is even; the sum of the odd terms is \( 24, \) and of the even terms is 30 and the last term exceeds the first by \( 10.5, \) then the number of terms in the series is
- A. 8
- B. 4
- C. 6 \)
- D. 10
Step-by-step solution
Let the number of terms be 2n. Sum of odd terms = n[a + (n-1)d] = 24, sum of even terms = n[a + nd] = 30. Subtracting gives nd = 6, so d = 6/n. The last term exceeds the first by (2n-1)d = 10.5 = 21/2. Substituting d gives 6(2n-1)/n = 21/2, solving yields n = 4, so 2n = 8.
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