Dezembro 29, 2019

por Kora

Qual é a soma da sequência $5, 10, 15, 20, 25, 30, 35, 40, 45, 50$ $5, 10, 15, 20, 25, 30, 35, 40, 45, 50$ ?

Responda:

275

Explicação:

This is an $Arithmetic sequence$ $color(blue)" Arithmetic sequence "$

The standard sequence being :

a , a+d , a+2d , a+3d , ............... , a+(n-1)d

where a , is the 1st term and d , the common difference.

The sum to n terms of the sequence is :

$color(red)(|bar(ul(color(white)(a/a)color(black)( S_n = n/2 [ 2a + (n - 1)d])color(white)(a/a)|)))$

here a = 5 , d = 10-5 = 15-10 = 5 and n = 10

$rArr S_(10) = 10/2[ 2xx5 + 9xx5 ] = 5 xx55 = 275$