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Arithmetic
Sequences & Series

A arithmetic sequence is a set of numbers where the next number is created by adding another number. A series is when you add up that sequence. Here you'll find more than a dozen solved problems. 

Which number belongs?

A sequence is given and you'll need to figure out if a certain number belongs in that sequence.  

Find "d"

In this problem you're given a sequence and asked to find the common difference. 

Find "d" (again!)

This sequence has fractions. It's a little harder to find the common difference. 

Find "d" given the formula for Tn. 

Given Tn = -7 + (n-1)(-2.5), find "d" 

Given a sequence, find the formula for Tn.  

Given terms -9, -1, 7, 15, 23 ... find  formula for Tn. 

Find the sum 

Find the sum of -5+(-7)+(-9)+...+(-19).  

Find the sum (again)

Given T1=-2; T3=7; and n=15. Find the sum.  

Find the sum (different)

Given T1=1/2; d=3; and n=19. Find the sum. 

Find T1, d & n. 

Given 107+130+153+...+981, find T1, d and n.  

Word Problem!! Saving money. 

On day one, Mike places 5c in a jar. The next day, he place 7c. Then 9c. Etc. How much will he have after 24 days?   

Three harder problems 

Q1. Find T1, d, and T20 giving a sequence. Q2. Find T1, d, and T20, given a more difficult sequence. .005;.05;.5; ...

Q3. Find Tn, Sn, T12, and S4 for this sequence: T1=2; d=3; n=4. 

Number and letters!

Determine the sum of 4k+11k+18k+...+74k.  

Word Problem - Harder!

2 weeks after opening, a fitness club has 870 members. After 8 weeks this grows to 1110. How many joined each week? And how many were there after week 1? 

Bonus exam question.

In an arith. series, S5=70 and S11=372. Determine T1 and d. And S30 and S50. Also the sum of the terms from 35 to 40.    

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