Question

How many terms are there in the A.P.?

`-1, 5/6, 2/3, 1/2,.....10/3`

Answer 1

In the given problem, we are given an A.P.

We need to find the number of terms present in it

So here we will find the value of n using the formula, `a_n = a + (n - 1)d`

 Here, A.P is `-1, 5/6, 2/3, 1/2,.....10/3`

The first term (a) = -1

The last term `(a_n) = 10/3`

Now

Common difference (d) = `a_1 - a`

`= -5/6 - (-1)`

`= -5/6 + 1``

`= (-5 + 6)/61

`= 1/6`

Thus, using the above mentioned formula, we get,

`10/3 = -1 + (n - 1) 1/6`

`10/3 +1 = 1/6 n - 1/6`

`13/3 + 1/6 = 1/6 n`

Further solving for n, we get

`(26 + 1)/6    = 1/6 n`

`n = 27/6 (6)`

n = 27

Thus n = 27

Therefore, the number of terms present in the given A.P is 27