How many terms are there in the A.P. 2/3, 1/2,1/3,.........., whose last term is - 17/3.
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AP : 2/3,1/2,1/3...
a = 2/3 , d = (1/2)-(2/3) = -1/6
Last term = -17/3
Tn = -17/3
a+(n-1)d = -17/3
2/3+(n-1)(-1/6) = -17/3
(n-1)(-1/6) = (-17/3)-(2/3)
(n-1)(-1/6) = -19/3
(n-1) = 6×19/3
n-1 = 38
n = 38+1 = 39
There are 39 terms in the Given AP
a = 2/3 , d = (1/2)-(2/3) = -1/6
Last term = -17/3
Tn = -17/3
a+(n-1)d = -17/3
2/3+(n-1)(-1/6) = -17/3
(n-1)(-1/6) = (-17/3)-(2/3)
(n-1)(-1/6) = -19/3
(n-1) = 6×19/3
n-1 = 38
n = 38+1 = 39
There are 39 terms in the Given AP
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