Answer:
Given,
AP of -1, -5/6, -2/3, -1/2, …
a1 = a = -1
a2 = -5/6
Common difference,
d = a2 – a1
= -5/6 – (-1)
= -5/6 + 1
= (-5+6)/6
= 1/6
an = a + (n – 1) d
an = -1 + (n – 1) 1/6
= -1 + 1/6n – 1/6
= (-6-1)/6 + 1/6n
= -7/6 + 1/6n
Put, an = 10/3
an = -7/6 + 1/6n = 10/3
1/6n = 10/3 + 7/6
1/6n = (20+7)/6
1/6n = 27/6
n = 27
Total 27 terms exists in the given A.P.