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1.

The n-th term of an arithmetic sequence with first term a and common difference d is given by:

Tn = a + n * d

Tn = 1/2 n (2a + d)

Tn = a * r^{n − 1}

Tn = a + (n - 1) * d

2.

In the arithmetic sequence (3, 7, 11, 15, ...), the common difference d and the 20th term (T₂₀) are respectively:

d = 5 and T₂₀ = 98

d = 4 and T₂₀ = 79

d = 4 and T₂₀ = 83

d = 3 and T₂₀ = 60

3.

The sum of the first n terms of an arithmetic sequence (Sn) is formulated as:

Sn = a * (1 - rⁿ) / (1 - r)

Sn = n * (a + d)

Sn = a / (1 - r)

Sn = n / 2 * [ 2a + (n - 1) * d ] = n / 2 * [ a + l ]

4.

The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:

r = 1/2

r = -1/2

r = 4

r = 2

Lesson 1 – Arithmetic and Geometric Sequences and Series — Lesson quiz