Arith & Geo Sequences and Series Summative

Front

What is the common difference in the arithmetic sequence 97, 86, 75, 64...?

Back

The common difference is -11.

Front

How do you find the 25th term of an arithmetic sequence with a1 = 5 and d = 0.5?

Back

The 25th term is 17.

Front

What is the recursive formula for the sequence 2, -6, 18, -54...?

Back

a_n = a_{n-1} * -3, a_1 = 2.

Front

Write the explicit equation for the sequence 30, 26, 22, 18...

Back

a_n = -4n + 30.

Front

What is the sum of the arithmetic series 2 + (-2) + (-6) + (-10)... up to S10?

Back

The sum S10 is -160.

Front

Define an arithmetic sequence.

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by a_n = a_1 + (n-1)d.

Front

Define a geometric sequence.

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term is given by a_n = a_1 * r^(n-1), where r is the common ratio.

Front

How do you find the sum of the first n terms of an arithmetic series?

Back

The sum S_n is given by S_n = n/2 * (a_1 + a_n).