Qual è la somma della sequenza # 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 #?

This is an# 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#