## anonymous one year ago WILL GIVE MEDAL!!!!! what is the sum of the arithmetic sequence 3,9,15.....if there are 22 terms ???

1. SolomonZelman

Ok, you start from n=1, and go up by 6 each time. For the sum you need the 22nd term. $$\large { \displaystyle{\rm a}_{n}={\rm a}_1+{\rm d}({\rm n}-1) }$$ $$\large { \displaystyle{\rm a}_{22}=3+{\rm 6}({\rm 22}-1) }$$ $$\large { \displaystyle{\rm a}_{22}=3+{\rm 6}(21) }$$ $$\large { \displaystyle{\rm a}_{22}=129 }$$

2. SolomonZelman

Then the sum of the first 22 terms (of this arithmetic sequence) is: $$\large { \displaystyle{\rm S}_{22}=\frac{ \left({\rm a}_1+{\rm a}_{22}\right) }{2} \times 22 }$$

3. SolomonZelman

$$\large { \displaystyle{\rm S}_{22}=\frac{ \left(3+129\right) }{2} \times 22 }$$