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Class 10 › Mathematics › Arithmetic Progressions
CBSE2026Class Class 10 · Mathematics2 Marks · Short✅ Verified
Find the sum of the first $28$ terms of an A.P. whose $n^{th}$ term is given by $a_n = 3n - 2$.
✅ Answer & Solution
Step 1: Put $n = 1$ to get the first term.
$$a_1 = 3(1) - 2 = 1$$
Step 2: Put $n = 28$ to get the $28^{th}$ term.
$$a_{28} = 3(28) - 2 = 84 - 2 = 82$$
Step 3: Use $$S_n = \frac{n}{2}(a_1 + a_n)$$
Step 4: $$S_{28} = \frac{28}{2}(1 + 82) = 14 \times 83 = 1162$$
Hence the sum of the first $28$ terms $= 1162$.