Question

efectuati: a)5+10+15+...+1000 b)8+16+24+...+4000 c)11+22+33+...+7700 d)4+8+12+16+...+400

Answer 1

a) a1 =5, an = 1000

an = 1000/5 = 200
a200 = 5 + (200-1)5 = 5 + 199x5 = 995 + 5 = 1000. (A)
S200 = a200 + a1 /2 x 200 = 1000 + 5 /2 x 200 = 1005/2 x 200 = 502.5 x 200 = 100500.

b) a1 = 8, r = 8

an = 4000/8 = 500
S500 = 500 + 8 /2 x 500 = 508/2 x 500 = 254 x 500 = 127000.

c) a1 = 11, r = 11.

an = 7700/11 = 700
S700 = 700+11 /2 x 700 = 711/2 x 700 = 355.5 x 700 = 248850

d) a1 = 4, r = 4

an = 400/4 = 100

S100 = 100+4 /2 x 100 = 104/2 x 100 = 52 x 100 = 5200.