Question

Как найти d в арифметической прогрессии?

Answer 1

aₙ = 2 + aₙ₋₁        a₁ = 1

a₂ = 2 + a₂₋₁ = 2 + a₁ = 2 + 1 = 3

a₂ = a₁ + d

d = a₂ - a₁ = 3 - 1 = 2

d = 2

a₁₀ = a₁ + 9d = 1 + 9 * 2 = 1 + 18 = 19

$S_{10}=\frac{a_{1}+a_{10}}{2}*10=(a_{1}+a_{10})*5=(1+19)*5=100\\\\Otvet:\boxed{d=2;a_{10}=19;S_{10}=100}$