Flashcards: Real Sequences — 11 cards

What defines an arithmetic sequence in terms of its terms' difference?

The difference between consecutive terms is a constant reason r.

What is the formula for the sum of terms from u_p to u_n in an arithmetic sequence?

The sum is $\frac{(n-p+1)(u_p+u_n)}{2}$.

What defines a geometric sequence in terms of its terms?

Each term is obtained by multiplying the previous term by a constant ratio q.

What is the sum formula for consecutive terms of a geometric sequence when q ≠ 1?

The sum is $u_p\frac{1-q^{n-p+1}}{1-q}$.

Arithmetic sequence: reason r

Sequence where each term increases by r.

Formula for arithmetic sequence

Un = u0 + nr or u1 + (n-1)r.

Sum of arithmetic terms

(n-p+1)(u_p + u_n)/2.

Geometric sequence: reason q

Sequence where each term multiplies by q.

Limit condition for q > 1

q^n tends to +∞ as n→∞.

Bounded sequence

Sequence with upper and/or lower bounds.

Monotone sequence

Sequence always increasing, decreasing, or constant.