Algebra
Arithmetic Progressions, Sum of Series
jee_main_2026_april_4_shift_2
Grade 12
Question:
The sum of the first 10 terms of the AP: 1, 3, 5, 7, ... is S. If the sum of the first 5 terms of the same AP is T, find S - 4T.
Step-by-Step Solution
Key Concept: Use AP sum formula: S_n = n/2[2a + (n-1)d].
Step 1: S_10 = 10/2[2(1) + (10-1)2] = 5[2 + 18] = 100. Step 2: S_5 = 5/2[2(1) + (5-1)2] = 5/2[2 + 8] = 5/2 × 10 = 25. Step 3: S_10 - 4S_5 = 100 - 100 = 0.
Correct Answer: 0
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