Question

A P. A (1. 5,9. ) tem 15 elementos. Calcule a soma de seus elementos

Answer 1

Resposta:

$\sf P.A.(1,5,9,...)\!\!:n=15.$

$\therefore$

$\sf a_n=a_1+(a_2-a_1)(n-1)$

$\sf a_{15}=1+(5-1)(15-1)$

$\sf a_{15}=1+4(14)$

$\sf a_{15}=1+56$

$\sf a_{15}=57$

$\therefore$

$\sf S_n=\dfrac{n(a_1+a_n)}{2}$

$\sf S_{15}=\dfrac{15(1+57)}{2}$

$\sf S_{15}=\dfrac{15(58)}{2}$

$\sf S_{15}=15(29)$

$\red{\sf S_{15}=435}\leftarrow\sf soma~dos~elementos.$

Answer 2

r: razão

r = a₂ - a₁

r = 5 - 1

r = 4

aₙ = a₁ + (n-1) . r

a₁₅ = 1 + (15 - 1) . 4

a₁₅ = 1 + 14 . 4

a₁₅ = 1 + 56

a₁₅ = 57

Sₙ = (a₁ + aₙ) . n/2

S₁₅ = (1 + 57) . 15 / 2

S₁₅ = (58) . 15 / 2

S₁₅ = 29 . 15

S₁₅ = 435