Question
Let a_1, a_2, a_3 be a harmonic progression with a_1=5 and a_ 20 =25. The least positive integer n for which a_n < 0, is
BITSAT
Mathematics
Sequences and Series
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 22
- B. 23
- C. 24
- D. 25
Answer
D. 25
Step-by-step solution
It is given that a_1, a_2, a_3 . are in HP. Therefore, 1 a_1 , 1 a_2 , 1 a_3 , .. are in AP. Let d be the common difference of the AP. 1 a_n = 1 a_1 +(n-1) d and 1 a_ 20 = 1 a_1 +19 d 1 a_n = 1 5 +(n-1) d and 1 25 = 1 5 +19 d 1 a_n = 1 5 +(n-1) d and d= -4 19 25 1 a_n = 1 5 - 4(n-1) 19 25 1 a_n = 95-4 n+4 19 25 a_n= 99-4 n 19 25 Now, a_n 99 n>24 3 4 n 25
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