Question

In arthmetic sequence;
a1+a4+a7+a10=50. then, a1+a2+a3...+a10=?​

Answer 1

125

Explanation:

For arithmetic sequence: aₙ = a₁ + (n-1)d Sₙ = n/2 * (a₁ + aₙ)

a1+a4+a7+a10 = a₁ + (a₁ + 3d) + (a₁ + 6d) + (a₁ + 9d) = 4a₁ + 18d = 2 * (2a₁ + 9d)

2 * (2a₁ + 9d) = 50

2a₁ + 9d = 25

a1+a2+a3...+a10 = 10/2 * (a₁ + a₁₀) = 5 * (a₁ + a₁ + 9d) = 5 * (2a₁ + 9d)

a1+a2+a3...+a10 = 5 * 25 = 125