Question

In progresia aritmetica cu a[3] = 25 si a[5] = 43, aflati ratia r, primul termen a[1], al 20-lea termen a[20] si suma S[20]

Answer 1

a[3] = a[1] + 2*r

a[5] = a[1] + 4*r

a[5] - a[3] = 2r

43-25 = 2r

2r = 18

deci r = 9

a[3] = a[1] + 2*r

a[1] = a[3] - 2r = 25 - 18 = 7

a[20] = a[1] + 19*r = 7 + 19*9 = 178

s[20] = 20*(a1 + a20)/2 = 10 *(7+178) = 1850