Question

Calcule a soma de 30° do termo p.a (1,3,5,7...)

Answer 1

Precisamos calcular an

$a_n=a_{30}=?\\ a_1=1\\ r=3-1=2\\ n=30\\ \\ Forma~~geral\\ \\ a_n=a_1+(n-1)r\\ \\ a_{30}=1+(30-1)(2)\\ a_{30}=1+(29)(2)\\ a_{30}=1+58\\ a_{30}=59$

Vamos calcular a soma

$a_n=59\\ a_1=1\\ n=30\\ \\ forma~~geral\\ \\ S_n={(a_1+a_n)n\over 2}\\ \\ S_{30}={(1+59)(30)\over2}\\ \\ S_{30}={(60)(30)\over2}\\ \\ S_{30}={1800\over2}\\ \\ S_{30}=900$

Answer 2

resolução!

r = a2 - a1

r = 3 - 1

r = 2

a30 = a1 + 29r

a30 = 1 + 29 * 2

a30 = 1 + 58

a30 = 59

Sn = ( a1 + an ) n / 2

Sn = ( 1 + 59 ) 30 / 2

Sn = 60 * 15

Sn = 900