Answer: 257
Explanation:
Given that:
a3 = 59
a7 = 103
The nth term of an Arithmetic Progression (A. P) is given by:
an = a1 + (n-1)d
Where a1 = first term of the sequence ;
d = common difference
Therefore a3 = 59 can be represented thus:
a3 = a1 + (3-1)d = 59
a3 = a1 + 2d = 59 - - - - (1)
a7 = 103
a7 = a1 + (7-1)d = 103
a7 = a1 + 6d = 103 - - - - - (2)
Subtracting (2) from (1)
(2d - 6d) = (59 - 103)
-4d = - 44
d = 11
Substitute d= 11 into (1)
a1 + 2d =59
a1 + 2(11) = 59
a1 + 22 = 59
a1 = 59 - 22
a1 = 37
The 21st term:
a21 = a1 + (21 - 1)d
a21 = 37 + 20(11)
37 + 220 = 257