Answer 1

Here, we have an A.P. whose n^th term (a_n), the sum of first n terms (S_n) and first term (a) are given. We need to find the number of terms (n) and the common difference (d).

Here,

First term (a) = 8

Last term (`a_n`) = 62

Sum of n terms (S_n) = 210

Now, here the sum of the n terms is given by the formula,

`S_n = (n/2)(a + l)`

Where a = the first term

l = the last term

So, for the given A.P, on substituting the values in the formula for the sum of n terms of an A.P., we get,

`210 = (n/2)[8 + 62]`

210(2) = n(70)

`n = 420/70`

n = 6

Also, here we will find the value of d using the formula,

`a_n = a + (n -1)d`

So, substituting the values in the above mentioned formula

62 = 8 + (6 -1)d

62 - 8 = (5)d

`54/5 = d`

`d = 54/5`

Therefore, for the given A.P `n = 6 and d = 54/5`