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

a_n = a + (n – 1) d

a_n = -1 + (n – 1) 1/6

= -1 + 1/6n – 1/6

= (-6-1)/6 + 1/6n

= -7/6 + 1/6n

Put, a_n = 10/3

a_n = -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.