Arithmetic Sequences and Algebra

Every arithmetic sequence can be written

Every arithmetic sequence can be written as xₙ = an + b, where 'a' is the common difference, 'b' is a constant, and 'n' represents the position. For e

When given specific terms at certain

When given specific terms at certain positions, we can find the algebraic form by setting up equations. For example, if 1st term = 5 and 10th term = 2

The sum of first n natural

The sum of first n natural numbers is given by: 1 + 2 + 3 + ... + n = n(n+1)/2. Gauss's method: Write the sum forward and backward, add corresponding

For sequence xₙ = an +

For sequence xₙ = an + b, sum of first n terms = ½an(n+1) + nb. Alternative method: Sum = ½ × number of terms × (first term + last term). Example: For

Special sequences have unique properties

Special sequences have unique properties: (1) Sum of first n odd numbers = n², (2) Sum of first n even numbers = n(n+1), (3) Some sequences contain al