Answer:
Step-by-step explanation:
The nth term of an Arithmetic sequence is expressed as;
Tn = a + (n-1)d
a is the first term
n is the numebr of terms
d is the common difference
If the 17th term has a value of 28, then
T17 = a + 16d = 28 ........ 1
If the 33rd term has a value of 78 then;
T33 = a+32d = 78 ...... 2
Solve simultaneously;
a + 16d = 28 ........ 1
a+32d = 78 ...... 2
Subtract
16d - 32d = 28-78
16d = 50
d = 50/16
d = 25/8
From 1;
a + 16d = 28
a + 16(25/8) = 28
a + 50 = 28
a = 28 - 50
a = -22
Get the 129th term
T129 = a + 128d
T129 = -22 + 128(25/8)
T129 = -22 +25(16)
T129 = -22+400
T129 = 378
Hence the 129th term is 378