Arithmetic Sequence Problems

Arithmetic Sequence Problems

**Page 1**

1.

The sum of the first p,q,r terms of an arithmetic progression are a,b,c, respectively, show that $\frac{a}{p}$ (q - r) + $\frac{b}{q}$ (r - p) + $\frac{c}{r}$ (p - q) = 0

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2.

In each of the following, list terms that continue a possible pattern.

Which of these sequences are arithmetic, which are geometric, and which are neither?

a) 8, 11, 14, 17, 20 ...

b) 1, 16, 81, 256, 625 ...

c) 5, 15, 45, 135, 405 ...

d) 2, 7, 12, 17, 22 ...

e) 1,1/2,1/4,1/8,1/16 ...

Find the 100$^{th}$ term and the $n^th$ term for each of the sequences in exercise 2.

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3.

In an arithmetic progression the eighth term is twice the fourth term and the 20th term is 40. find the common difference and the first term

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4.

A triangle has its three angles in Arithmetic Progression. If the largest angle is 108 degrees, find angles ?

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5.

How would you solve an arithmetic sequence with no $a_1$ and no common difference? Find the 23rd term of the arithmetic sequence if $a_18$=26 and $a_96$=65.

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6.

What are the practical applications of arithmetic progression?

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