10. Tentukan suku kesepuluh dari barisan aritmatika jika S4 = 20 dan S7 = 56 ! Jawablah dengan benar dan mudah dipahami

S4=20
S7 =56

Sn = n/2 ( 2×u1 + (n-1)×b)
20 = 4 /2 ( 2×u1 + (4-1)×b)
20 = 2× ( 2×u1 + 3×b)
20 = 4 u1 + 6 b.........(1)

Sn = n/2 ( 2×u1 + (n-1)×b)
56 = 7 /2 ( 2×u1 + (7-1)×b)
56 = 7/2× ( 2×u1 + 6×b)
56 = 7 u1 + 21 b....................(2)

Eliminasi (1) dan (2)

20 = 4 u1 + 6 b................... .(x7)
56 = 7 u1 + 21 b....................(x4)

140 = 28 u1 + 42 b................... .
224 = 28 u1 + 84 b....................
---------------------------- -
-84 = -42b
-84/-42 = b
2 =b
Subsitusikn b =2 ke prsamaan (1)

20 = 4 u1 + 6 b
20 = 4 u1 + 6 ×2
20 = 4u1 +12
20-12 = 4u1
8 = 4u1
8/4 = u1
2 = u1

Suku ke 10 => u10

Un
= u1 +(n-1)×b
= 2 + ( 10-1)×2
= 2+18
=20