# Thread: geomertric and arithmetric sequences

1. ## geomertric and arithmetric sequences

a geometric sequence of posotive terms has first term 2 and the sum of the first three terms is 266 calculate the common ratio

an arithmetric sequense A has first term a and a common difference of 2 and a geometric sequence B has first term a and common ratio 2. the first four terms of each sequence have the same sum. obtain the value of a

any help would be appreciated

2. Originally Posted by hmmmm
a geometric sequence of posotive terms has first term 2 and the sum of the first three terms is 266 calculate the common ratio
$\displaystyle 2 + 2r + 2r^2 = 266$

solve for $\displaystyle r$

an arithmetric sequense A has first term a and a common difference of 2 and a geometric sequence B has first term a and common ratio 2. the first four terms of each sequence have the same sum. obtain the value of a
$\displaystyle a + (a+2) + (a+4) + (a+6) = a + 2a + 4a + 8a$

solve for $\displaystyle a$

3. 1) $\displaystyle a_1=2, \ a_2=2r, \ a_3=2r^2$

$\displaystyle a_1+a_2+a_3=266\Rightarrow r^2+r-132=0$ and you have to solve the quadratic.

2) $\displaystyle a+(a+2)+(a+4)+(a+6)=a+2a+4a+8a$

Now find a.

### arithmetric sequences

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