4.The sum to 'n' terms of an arithmetic sequence is 4n² - 2n. i) Write the first term of the sequence.
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Given that
the sum of n terms of an arithmetic sequence
Sₙ = 4n² + 3n
So, nᵗʰ term of the sequence
Tₙ = Sₙ — Sₙ_₁
= (4n² + 3n) — {4(n — 1)² + 3(n — 1)}
= 4n² + 3n — {4(n² + 1 — 2n) + 3(n — 1)}
= 4n² + 3n — {4n² + 4 — 8n + 3n — 3}
= 4n² + 3n — 4n² — 4 + 8n — 3n + 3
= 8n — 1
So first term,
T₁ = 8(1) — 1 = 8 — 1 = 7
Hope it will help you
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