Question

Obtenha o valor da P A em que o vigésimo termo é 2 e a soma dos 50 termos iniciais é 650

Answer 1

P.A.(-36,-34,-32,-30,-28,-26,-24,-22,-20,-18,-16,-14,-12,-10,-8,-6,-4,-2,0,2,4,..)
a 20 = 2
S 50 = 650
a 20 = a 1 + (n - 1 ).r
a 20 = a 1 + (20 - 1).r
 2 = a 1 + 19.r
a 1 + 19 r = 2
a 1 = 2 - 19 r  ( I )
a 50 = a 1 + (n- 1 ).r
a 50 = a 1 + (50 - 1 ).r
a 50 = a 1 + 49.r
a 50 = 2 - 19 r + 49 r
a 50 = 2 + 30 r  ( II )
S n = n . (a 1 + a n ) / 2
S 50 = 50 . (a 1 + a 50 ) / 2
650 = 50 .(2 - 19 r + 2 + 30 r) / 2
650 . 2 = 50.(4 + 11 r)
1300 = 50.(4 + 11 r)
1300/50 = 4 + 11 r
26 = 4 + 11 r
26 - 4 = 11 r
22 = 11 r
22/11 = r
r = 2
a 1 = 2 - 19.r
a 1 = 2 - 19.2
a 1 = 2 -  38
a 1 = - 36