Question

Fie suma de nr. naturale consecutive
S=5+9+13+...101
a)Aflați numărul de termeni a acestei sume .
b)Calculați valoarea sumei S.

Answer 1

Nr termeni=(101-5):4+1=104:4+1=26+1=27. S=(101+5)x27/2=106x27/2=53x27=1431

Answer 2

S=5+9+13+...101

a) an=a1+(n-1)·r;     an=101; a1=5 si  r=4

101=5+(n-1)·4

n=(101-5+4):4=100:4

n=25 termeni

sau a1=1·4+1

a2=2·4+1

a3=3·4+1

.................

an=n·4+1

deci, n·4+1=101

=> n=100:4

n=25 termeni

b) S=(5+101)·25/2=106·25/2

S=53·25

S=1325