## anonymous one year ago Find S10 for 2 + 5 + 8 +... @mathstudent55 i got 270, is that right?

1. zzr0ck3r

$$\sum_{n=1}^{10}(2+3(n-1))=\sum_{n=1}^{10}-1+3n=\sum_{n=1}^{10}-1+3\sum_{n=1}^{10}n=-10+3\dfrac{10*11}{2}=\\-10+3*5*11=165-10=155$$

2. mathstudent55

$$a_1 = 2$$, $$a_2 = 5$$, and $$a_3 = 8$$ We are dealing with an arithmetic series. $$d = a_2 - a_1 = 5 - 2 = 3$$ $$a_n = a_1 + (n - 1)d$$ $$a_{10} = 2 + (10 - 1)3 = 2 + 9(3) = 29$$ $$S_n = \dfrac{n(a_1 + a_n)}{2}$$ $$S_n = \dfrac{10(2 + 29)}{2} = 155$$

3. Jack1

that seems... right...