Arithmetic and geometric sequences, summation notation
Find the 5th term of arithmetic sequence: 2, 5, 8, 11...
Common difference d=3, so a₅ = a₁ + (5-1)d = 2 + 4×3 = 14
What is the common ratio of geometric sequence: 3, 6, 12, 24...?
Divide any term by previous: 6/3 = 2, 12/6 = 2, etc.
Write sum using sigma notation: 1 + 3 + 5 + 7 + 9
Odd numbers can be represented as 2n-1
Find sum of first 10 terms of arithmetic series: 1 + 4 + 7 + ...
Sₙ = n/2 × (2a₁ + (n-1)d) = 10/2 × (2×1 + 9×3) = 5 × 29 = 145
What is the 7th term of geometric sequence with a₁=2 and r=3?
aₙ = a₁ × rⁿ⁻¹ = 2 × 3⁶ = 2 × 729 = 1458