Question

What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, ........? 
 

• A. 820
• B. 840
• C. 860
• D. 880

Hint:

Always remember the two equivalent AP sum formulas: $S_n = \frac{n}{2}[2a + (n-1)d]$ and $S_n = \frac{n}{2}(a+l)$.

Answer 1

The Correct Option is A

- Step 1: Identify the sequence parameters - First term $a = 3$, common difference $d = 4$. 

- Step 2: Number of terms - $n = 20$. 

- Step 3: Using sum formula - For arithmetic progression: \[ S_n = \frac{n}{2} \left[ 2a + (n-1)d \right] \] Substitute: \[ S_{20} = \frac{20}{2} \left[ 2(3) + (20-1)(4) \right] \] 

- Step 4: Simplify - \[ S_{20} = 10 \left[ 6 + 19 \times 4 \right] = 10 \left[ 6 + 76 \right] = 10 \times 82 = 820 \] 

- Step 5: Alternate check - Last term $l = a + (n-1)d = 3 + 76 = 79$, so: \[ S_{20} = \frac{n}{2}(a + l) = 10(3 + 79) = 10 \times 82 = 820 \] 

- Step 6: Conclusion - Sum is $820$, matching option (1).