Matematica - p.a.
1) Numa P.A. ( √2 ; x ; 6√2 ; ... ) Calcular a50
x = ( a1 + a3 ) / 2 x = ( 2 + 62 ) / 2 x = 722
r = a2 – a1 r = ( 722 ) - 2 r = 522
an = a1 + ( n – 1 ) . r a50 = 2 + ( 50 – 1 ) . 522 a50 = 2 + 49 . 522 a50 = 2 + 24522 a50 = 24722
2) Numa P.A. ( 33 ; x ; 63 ; ... ) Calcular a30
x = ( a1 + a3 ) / 2 x = ( 33 + 63 ) / 2 x = 932
r = a2 – a1 r = 932 - 33 r = 332
an = a1 + ( n – 1 ) . r a30 = 33 + ( 30 – 1 ) . 332 a30 = 33 + 29 . 332 a30 = 33 + 8732 a30 = 9332
3) Numa P.A. ( 12 ; 1 ; 32 ; ... ) Calcular a15
r = a2 – a1 r = 1 – 12 r = 12
an = a1 + ( n – 1 ) . r a15 = 12 + ( 15 – 1 ) . 12 a15 = 12 + 14 . 12 a15 = 12 + 7 a15 = 152
4) Numa P.A. ( -8 ; -12 ; ... ) Calcular a18
r = a2 – a1 r = -12 – ( -8 ) r = -12 + 8 r = -4
an = a1 + ( n – 1 ) . r a18 = -8 + ( 18 – 1 ) . ( -4 ) a18 = -8 + 17 . ( -4 ) a18 = -8 – 68 a18 = -76
5) Numa P.A. ( -8 ; -9 ; -10 ; ... ) Calcular a100
r = a2 – a1 r = -9 – ( -8 ) r = -9 + 8 r = -1
an = a1 + ( n – 1 ) . r a100 = -8 + ( 100 – 1 ) . ( -1 ) a100 = -8 + 99 . ( -1 ) a100 = -8 – 99 a100 = -107
6) S50 = ? (no exercício 1)
a50 = 247√22
S50 = ( a1+ an ) . n2
S50 = ( (2 + 247√22 ) . 50 ) / 2
S50 = ( 249√22 . 50 ) / 2
S50 = 6225√22
7) S51 = ? (no exercício 2)
an = a1 + ( n – 1 ) . r a51 = 33 + ( 51 – 1 ) . 332 a51 = 33 + 50 . 332 a51 = 33 + 753 a51 = 783
Sn = ( a1+ an ) . n2
S51 = ( a1+ a51 ) . 512
S51 = ( 33 +783 ) . 512
S51 = ( 813 ) . 512
S51 = 41313 2
8) S15 = ? (no exercício 3)
a15 = 152
Sn = ( a1+ an ) . n2
S15 = ( a1+ a15 ) . 152
S15 = ( 12 + 152 ) . 152
S15 = 8 . 152
S15 = 1202
S15 = 60
9) S20 = ? (no exercício 4)
an = a1 + ( n – 1 ) . r a20 = -8 + ( 20 – 1 ) . ( -4 ) a20 = -8 + 19 . ( -4 ) a20 = -8 – 76 a20 = -84
Sn = ( a1+ an ) . n2
S20 = ( a1+ a20 ) . 202
S20 = ( -8 +(-84) ) . 202
S20 = ( -8 - 84) . 202
S20 = ( -92 ) .