Question

( deret aritmetika )
dalam deret aritmetika diketahui : U5 = 13 dan U9 = 21
tentukan :
a . nilai a dan b
b . U10
c . S50

Answer 1

A+4b=13
a+8b=21
--------------- -
4b = 8
b=2

a+8=13
a=13-8=5

U10=5+9.2=5+18=23
S50=25(10+49.2)=25.(10+98)=25.108=2700

Answer 2

A) beda = (21-13) / (9-5) = 8/4 = 2
a+4b = 13
a+4(2) = 13
a+8 = 13
a = 5

b) Un = a+(n-1)b
U10 = 5+(10-1)2
U10 = 5+9.2
U10 = 5+18
U10 = 23


c) Sn = n/2(2a+(n-1)b)
S50 = 50/2 ( 2.5+(50-1)2)
= 25(10+49.2)
= 25(10+98)
= 25(108)
= 2700