**NCERT/CBSE MATHS Class 10 Ex-5.2 Q No.15**** Solutions : **** For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?**

Hy Friends Welcome On **NCERT MATHS SOLUTIONS** !! Today we are going to solve the Question : **”**** For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?****” **of** Exercise 5.2 Question No 15 Solutions (Arithmetic Progressions)** of Class 10th, which will prove to be very helpful for you.

**CBSE/NCERT MATHS Class 10 Ex-5.2 Q No. 15 Solutions**

If you are a student of CBSE, today we are going to give you the **CBSE / NCERT** **Chapter : Arithmetic Progressions ** **Exercise 5.2 Question No – 15** **Solutions** . Hope you like this post about Class 10th Maths Solution.

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**Arithmetic Progressions CHAPTER : 5**

n this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term.

Suppose, a_{1}, a_{2}, a_{3}, ……………., a_{n} is an AP, then;_{ }the **common difference “ d ”** can be obtained as; In this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term.

**a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d**

**Exercise- 5.2 Question No. 15 :**

** For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?**

**Class 10 Exercise 5.2 Question No. 15 Solutions**

63, 65, 67, …

*a* = 63

*d* = *a*_{2} − *a*_{1} = 65 − 63 = 2

**n ^{th} term of this A.P. = a_{n} = a + (n − 1) d**

*a*

_{n}= 63 + (

*n*− 1) 2 = 63 + 2

*n*− 2

*a*

_{n}= 61 + 2

*n*…

**(i)**

3, 10, 17, …

*a*= 3

*d*=

*a*

_{2}−

*a*

_{1}= 10 − 3 = 7

*n*

^{th}term of this A.P. = 3 + (

*n*− 1) 7

*a*

_{n}

_{ }= 3 + 7

*n*− 7

*a*

_{n}= 7

*n*− 4 …

**(ii)**

**It is given that,**

*n*^{th}term of these A.P.s are equal to each other.**Equating both these equations, we obtain**

61 + 2

*n*= 7

*n*− 4

61 + 4 = 5

*n*

5

*n*= 65

*n*= 13

Therefore,

**13**

^{th}terms of both these A.P.s are equal to each other.## **OR**

**Solution:**

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