Which of the term of A.P. 5, 2, − 1, ...... is − 49?

We have been given an arithmetic progression 5, 2, − 1,.. 

It is known that the 𝑛𝑡ℎ term of an AP is given by 𝑎_𝑛 = 𝑎 + (𝑛 − 1)𝑑

where a_n  is the n^th term, is the first term, a is the first term, n is term to be found  and 𝑑 is the common difference of the A.P

Here, we need to find '𝑛'. We can see that first term; 𝑎 = 5,

We know that the common difference of an 𝐴𝑃 is the difference between its two consecutive terms.

⇒ Common difference; 𝑑 = 2 − (5) ⇒ 𝑑 =− 3 

Now, putting 𝑎 in the above formula, 

we get, 

− 49 = 5 + (𝑛 − 1) ×− 3

 ⇒ − 49 − 5 = (𝑛 − 1) ×− 3

⇒ 𝑛 = 18 + 1 

⇒ 𝑛 = 19 

Hence, − 49 is the 19^𝑡ℎ term of the given 𝐴. 𝑃.