Question

1)Numa P.A de razão 3,o 7 termo é 21 e qual é o 1 termo?


2)Quantos termos tem a P.A (5,10.......785) ?

Com calculos por favor!

Answer 1

$P.A.\to Formula\to a_{n} = a_{1} +(n-1)*r$


$1)P.A\to r=3; a_{7} =21;n=7; a_{1} =?\\\\\\21=a_{1} +(7-1)*3\to \\\\21=a_{1} +6*3\to \\\\21=a_{1} +18\to \\\\21-18=a_{1} \to \\\\a_{1} =3$


$2)P.A.(5,10,...,785)\\ \\a_{1} =5;a_{n} =785;r=5;n=?\\\\\\785=5+(n-1)*5\to \\\\785=5+5n-5\to \\\\785=5n\to \\\\\frac{785}{5} =n\to\\ \\n=157$