The 8th term of an arithmetic sequence is 12 and its 12th term is 8.
What is the algebraic expression for this sequence?
Answers
Mark as BRAINLIEST.
8 term = a+7d = 12
12 term = a+11d = 8
Solving these two equations, we get,
Subtracting both we get,
4d = -4
d = -1
Putting d=-1, we get a= 19
Then arithmetic progression will be,
19, 18, 17, 16, 15......
Given , 8th term is 12 and 12th term is 8
nth term of a.p. is given by ,
tn = a + ( n -1) d
therefore ,
t8 = a + ( 8-1) d
t8 = a +7d
but , t8 = 12
therefore , a +7d = 12 --------( 1 )
also ,
t12 = a + ( 12 -1) d
t12 = a + 11d
but , t12 = 8
therefore ,
a + 11d = 8 -------- ( 2 )
subtracting eq 1 from eq 2
a + 11d = 8
a +7d = 12
-----------------
4d = -4
d = -1
putting this value in equation 1 we get
a +7(-1) = 12
a - 7 =12
a = 19
therefore the general equation for any nth term becomes
tn = a + ( n -1) d
tn = 19 + ( n -1) (-1)
tn = 19 - n + 1
tn = 20 - n