Determine a soma e o produto dos 9 elementos iniciais de uma P A (a1, a2, a3) em que a2 = 15 e a4 = 5

Determine a soma e o produto dos 9 elementos iniciais de uma P A (a1, a2, a3) em que a2 = 15 e a4 = 5



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    De uma PA sabemos que:

    a_3=frac{a_2+a_4}{2} a_3=frac{15+5}{2} a_3=frac{20}{2} boxed{a_3=10}

    Agora, ficou assim:

    PA(a_1,15,10) r=a_3-a_2 r=10-15 boxed{r=-5}

    Soma dos 9 primeiros termos

    a_9=a_1+8r a_9=20+8*-5 a_9=20-40 boxed{a_9=-20}

    soma

    S_9=frac{(a_1+a_9)*9}{2} S_9=frac{(20-20)*9}{2} S_9=frac{0*9}{2} S_9=frac{0}{2} boxed{S_9=0}

    Produto

    P_9=a_1*a_2*a_3*a_4*a_5*a_6*a_7*a_8*a_9 P_9=20*15*10*5*0*-5*-10*-15*-20 boxed{P_9=0}

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    Determinar a razo:

    an = ak + ( n — k ) *r
    15= 5 + ( 2 — 4 ) * r
    15= 5 — 2*r
    15- 5 = -2 *r
    10/ -2 = r
    r= -5

    Razo = -5

    ========
    Determinar a1

    an = a1 + ( n — 1 ) * r
    15= a1 + ( 2 — 1 ) * ( -5 )
    15= a1 + 1 *( -5 )
    15= a1 — 5
    15+ 5 = a1
    a1= 20

    ============

    Soma dos termos:

    a1 = 20
    a2 = 15

    Sn = ( a1 + an ) * n/ 2
    Sn = ( 20 — 20 ) * 9/ 2

    Sn = 0 . 4,5

    Sn = 0


    Soma = 0

    ============

    Produtos dos 9 primeiros termos:

    PA ( 20 ; 15 ; 10 ; 5 ; 0 ; -5 ; -10 ; -15 ; -20)

    Produto = 0


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