Diketahui suatu barisan aritmatika dengan U7 = 100 dan U15 = 172. Tentukan A.Suku pertama B. beda C.U11 D.S11

Diketahui :
U7 = 100
U15 = 172

Ditanya :
A. U1 = ?
B. b = ?
C. U11 = ?
D. S11 = ?

Jawab :
B). Un = a + (n-1) b
U7 = a + (7-1) b
100 = a + 6b........... pers 1
U15 = a + (15-1) b
172 = a + 14b........ pers 2

Eliminasi :
100 = a + 6b
172 = a + 14b
-------------------- -
-72 = - 8b ( dibagi -8)
9 = b


A). Subtitusi b= 9 ke pers 1 :
100 = a + 6b
100 = a + 6 (9)
100 = a + 54
100-54 = a
46 = a

U1 = a = 46


C). Un = a + (n-1) b
U11= 46 + (11-1) 9
= 46 + 10 × 9
= 46 + 90
= 136

D). Sn = n/2 [ 2a + (n-1) b ]
S11 = 11/2 [ 2(46) + (11-1) 9 ]
= 5,5 [ 92 + (10) 9 ]
= 5,5 ( 92 + 90 )
= 5,5 (182)
= 1.001