# The First Term of an A.P. is 5 and Its 100th Term is -292. Find the 50th Term of this A.P. - Mathematics

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

#### Solution

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

We need to find the 50th term

Here

a = 5

a_100 = -292

Now, we will find 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

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 19 | Page 25
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