The first term of an A.P. is 5 and its 100^{th} term is -292. Find the 50^{th} term of this A.P.

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#### Solution

In the given problem, we are given 1^{st} and 100^{th}^{ }term of an A.P.

We need to find the 50^{th} term

Here

a = 5

`a_100 = -292`

Now, we will find *d *using the formula `a_n = a = (n - 1)d`

So,

Also

`a_100 = a + (100 - 1)d`

-292 = a + 99d

So to solve for d

Substituting a = 5 we get

-292 = 5 + 99d

-292 - 5 = 99d

`(-297)/99 = d`

d = -3

Thus

a = 5

d = -3

n = 50

Substituting the above values in the formula `a_n = a + (n - 1)d`

`a_50 = 5 + (50 - 1)(-3)`

`a_50 = 5 - 147`

a_50 = -142

Therefore `a_50 = -142`

Concept: nth Term of an AP

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