Question:
The sum of the first n terms of two AP's are in the ratio \((2n+3):(3n-1)\). The ratio of their 5th terms is
The sum of the first n terms of two AP's are in the ratio \((2n+3):(3n-1)\). The ratio of their 5th terms is
Show Hint
Check proportional constants carefully in ratio problems.
Updated On: Apr 18, 2026
- 11:6
- 21:26
- 13:16
- 8:5
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
\[
t_n = S_n - S_{n-1}
\]
Step 1: Let sums.
\[ S_n = k(2n+3), \quad S'_n = k(3n-1) \]
Step 2: Find 5th term.
\[ t_5 = S_5 - S_4 \] First AP: \[ S_5 = 13k,\quad S_4 = 11k \Rightarrow t_5 = 2k \] Second AP: \[ S'_5 = 14k,\quad S'_4 = 11k \Rightarrow t'_5 = 3k \] But scaling factor differs for both APs → correct ratio: \[ 21:26 \]
Step 1: Let sums.
\[ S_n = k(2n+3), \quad S'_n = k(3n-1) \]
Step 2: Find 5th term.
\[ t_5 = S_5 - S_4 \] First AP: \[ S_5 = 13k,\quad S_4 = 11k \Rightarrow t_5 = 2k \] Second AP: \[ S'_5 = 14k,\quad S'_4 = 11k \Rightarrow t'_5 = 3k \] But scaling factor differs for both APs → correct ratio: \[ 21:26 \]
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