Question

PLEASE ANSWER please!!! im desperate im asking again

Given the nth term for each arithmetic

sequence, find the sum of the first 12 terms.

1. an = 4n + 1

2. an = 7 − 5n

3. an = 3 − 8n

4. an = 4n − 6

5. an = n + 1/2

Answer 1

• 1. 324
• 2. -306
• 3. -588
• 4. 246
• 5. 84

Explanation:

Sum of the first n terms of AP

• Sₙ = 1/2n(a₁ + aₙ)

The sum of the first 12 terms of AP

• S₁₂ = 1/2*12*(a₁ + a₁₂) = 6(a₁ + a₁₂)

1. aₙ = 4n + 1

• a₁ = 4 + 1 = 5
• a₁₂ = 4*12 + 1 = 49
• S₁₂= 6(5 + 49) = 324

2. aₙ = 7 - 5n

• a₁ = 7 - 5 = 2
• a₁₂ = 7 - 5*12 = -53
• S₁₂= 6(2 - 53) = -306

3. aₙ = 3 - 8n

• a₁ = 3 - 8 = -5
• a₁₂ = 3 - 8*12 = -93
• S₁₂= 6( -5 -93 ) = -588

4. aₙ = 4n -6

• a₁ = 4 - 6 = -1
• a₁₂ = 4*12 - 6 = 42
• S₁₂= 6(-1 + 42) = 246

5. aₙ = n + 1/2

• a₁ = 1 + 1/2 = 1.5
• a₁₂ = 12 + 1/2 = 12.5
• S₁₂= 6(1.5 + 12.5) = 84