Question

numa pa a19= 70 e r=7 determine: 1° termo, 10º termo e o 20° termo

Answer 1

A Progressão aritmética (P.A) é determinada por:

⇒ $a_{19}=70$
⇒ $r=7$

a) Calculando o $a_{1}$:

$a_n=a_k+\left(n-k\right)r\\a_{19}=a_1+\left(19-1\right)\cdot 7\\70=a_1+\left(18\cdot 7\right)\\70=a_1+126\\a_1=70-126\\\boxed{\bold{a_1=-56}}$

b) Calculando o $a_{10}$:

$a_n=a_k+\left(n-k\right)r\\a_{19}=a_{10}+\left(19-10\right)\cdot 7\\70=a_{10}+\left(9\cdot 7\right)\\70=a_{10}+63\\a_{10}=70-63\\\boxed{\bold{a_{10}=7}}$

c) Calculando o $a_{20}$:

$a_n=a_k+\left(n-k\right)r\\a_{20}=a_{19}+\left(20-19\right)\cdot 7\\a_{20}=70+\left(1\cdot 7\right)\\a_{20}=70+7\\\boxed{\bold{a_{20}=77}}$