Sum of an AP a=1, d=2, n=5.

**The reasoning** In an Arithmetic Progression (AP), we find the sum using the formula: **Sₙ = n/2 × [2a + (n-1)d]** Given: a = 1 (first term), d = 2 (common difference), n = 5 (number of terms) Let's substitute: S₅ = 5/2 × [2(1) + (5-1)(2)] S₅ = 5/2 × [2 + 4(2)] S₅ = 5/2 × [2 + 8] S₅ = 5/2 × 10 S₅ = **25** You can verify: the sequence is 1, 3, 5, 7, 9 → sum = 25 ✓ **Why the wrong options tempt you** **A) 11** — You might've added just a and d incorrectly or confused it with the last term calculation. **B) 15** — Common error: using n = 3 instead of n = 5, or miscalculating (n-1)d. **D) 30** — You probably multiplied n × (a + d) = 5 × 6, forgetting the proper AP sum formula. **Quick takeaway** For AP sums, always use **Sₙ = n/2 × [2a + (n-1)d]** — think of it as "number of terms times the average of first and last term."