Question

Data a P.A ( X-5, 8, 2x-6 ) determina o décimo primeiro termo e a soma dos 15 primeiros termos

Answer 1

$(x-5, 8, 2x-6)$

$8=\dfrac{x-5+2x-6}{2} \iff 3x-11=16 \iff 3x=27 \iff x=9$

$(4, 8, 12)$

$r=8-4 \iff r=4$

$a_{10}=a_1+9r \iff a_{10}=4+9\cdot4 \iff a_{10}=4+36 \iff a_{10}=40$

$a_{15}=a_1+14r \iff a_{15}=4+14\cdot 4 \iff a_{15}=4+56 \iff a_{15}=60$

$S_{15}=\dfrac{(a_1+a_{15})\cdot15}{2}=\dfrac{(4+60)\cdot15}{2} \iff S_{15}=\dfrac{64\cdot15}{2}$

$S_{15}=\dfrac{960}{2} \iff S_{15}=480$

Answer 2

a₂-a₁=a₃-a₂

8-(x-5)=2x-6-8

8-x+5=2x-14

2x+x=13+14

3x=27

x=27/3

x=9

(9-5,8,2.9-6)=(4,8,12)

r=4

a₁₅=a₃+12r

a₁₅=12+12.4

a₁₅=12+48

a₁₅=60

Sₙ=n(a₁+aₙ)/2

S₁₅=15(a₁+a₁₅)/2

S₁₅= 15(4+60)/2

S₁₅= 15.64/2

S₁₅=15.32

S₁₅=(10+5).32=320+160=480