7.2 Arithmetic sequences practice 2

The first term of an arithmetic sequence is [math]2017[/math]. The [math]2017^{th}[/math] term is 1. What is the [math]200^{\text{th}}[/math] term of this sequence?

How many terms are in the arithmetic sequence [math]40, 33, 26,\cdots, -3964[/math]?

The sequence [math]\log_{12}{162}, \log_{12}{x}, \log_{12}{y}, \log_{12}{z}, \log_{12}{1250}[/math] is an arithmetic sequence. Find [math]x, y[/math], and [math]z[/math].

An arithmetic progression is such that the sum of the first 8 terms is 424, and the sum of the first 10 terms is 650. Find the fifth term.

An arithmetic sequence has 5 and 13 as its two terms respectively

(a) Write down, in terms of [math]n[/math], an expression for the [math]n^{\text{th}}[/math] term [math]a_n[/math]

(b) Find the number of terms of the sequence which are less than 400.

Given that [math]k^2+ 4, 29, 3k [/math] are consecutive terms of an arithmetic sequence, find [math]k[/math]. (negative)

The ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is [math]\dfrac {6}{13}[/math] If each term of this sequence is positive, and the product of the first term and the third term is [math]32[/math], find the sum of the first [math]100[/math] terms of this sequence.

(Calculator) Consider the sequence [math]3, 7, 11, 15,\cdots, 995[/math]

(a) Find the number of terms in this sequence.

(b) Find the sum of this sequence.

(c) Create a new sequence by removing every third term, that is [math]11, 23, 35,\cdots[/math]. Find the sum of the remaining terms in the sequence.

Given the sequence [math] 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, 9\sqrt{2},\cdots[/math]

(a) If the [math]20^{\text{th}}[/math] term is [math]a\sqrt{2}[/math], find the value of [math]a[/math].

(b) If the sum of the first 30 terms is [math]b\sqrt{2}[/math], find the value of [math]b[/math].

A [math]28.5 m[/math] length of rope is cut into pieces whose lengths are in arithmetic progression with a common difference of [math]d[/math] m. Given that the lengths of the shortest and longest pieces are [math]1 m[/math] and [math]3.75 m[/math] respectively, find the number of pieces and the value of [math]d[/math].