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arithmetic and geometric sequences


iheartmath

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I've been studying for an IB math midterm and chapter 2 (arithmetic/geometric sequences) is giving me a head ache. The problems below are from my IB book so I know the answers because they are given in the back. Can anyone please please please explain to me how to work these problems? I want to ace my midterm and get an A+ this semester :) Your help is muchly appreciated!!!

1. Find the first term of the sequence 4,4√3,12,12√3,…. which exceeds 4800.

2. Find the sum of the multiples of 7 between 0 and 100

3. Find the sum of the integers between 1 and 100 which are not divisible by 3

4. Five consecutive terms of an arithmetic sequence have a sum of 40. The product of the first, middle, and last terms is 224. Find the terms of the sequence.

5. Find the sum of √7+7+7√7+49+⋯to 12 terms.

6. Let S_n be the sum of an infinite geometric sequence such that S_1=3 and S_2=4

a. State the first term S_n

b. Calculate S_5

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