Question

the 8th term of an arithmetic sequence is 12 and its 12 term is 8 what is algebraic expression of the sequence

Answer 1

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