Question

determine: a) o 20• termo PA (2,7..) b) o 7• termo de PA (1,2..) c) o 100• termo da PA (5,8...,98) e) a razao da PA (a1, a2,...) em que a1 =17 e a32 =-8

Answer 1

→ Legenda:

⇒ an = termo n (qualquer)
⇒ ak = termo k (qualquer)
⇒ r = razão da P.A
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→ Formula da P.A:

$an=ak+\left(n-k\right)\cdot r$
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a)
a1 = 2
a2 = 7

$r=a2-a1\\r=7-2\\r=5$

$an=ak+\left(n-k\right)\cdot r\\a20=a1+\left(20-1\right)\cdot 5\\a20=2+\left(19\cdot 5\right)\\a20=2+95\\\boxed{\bold{a20=97}}$
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b)
a1 = 1
a2 = 2

$r=a2-a1\\r=2-1\\r=1$

$an=ak+\left(n-k\right)\cdot r\\a7=a1+\left(7-1\right)\cdot 1\\a7=1+6\\\boxed{\bold{a7=7}}$
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c)
a1 = 5
a2 = 8

$r=a2-a1\\r=8-5\\r=3$

$an=ak+\left(n-k\right)\cdot r\\a100=a1+\left(100-1\right)\cdot 3\\a100=5+\left(99\cdot 3\right)\\a100=5+297\\\boxed{\bold{a100=302}}$
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d)
a1 = 17
a32 = -8

$an=ak+\left(n-k\right)\cdot r\\a32=a1+\left(32-1\right)\cdot r\\-8=17+31r\\31r=-8-17\\31r=-25\\\boxed{\bold{r=-25\div 31}}$