Check Whether –150 is a Term of the AP: 11, 8, 5, 2... | Class 10 Maths AP Question Solution
Chapter: Arithmetic Progression (AP)
📚 Class: 10th Mathematics (NCERT Based)
Aaj hum solve karenge ek important question Arithmetic Progression (AP) se:
Check whether –150 is a term of the AP: 11, 8, 5, 2…
🎥 Watch Detailed Video Solution:
Yeh question Class 10 Maths Chapter Arithmetic Progression ka hai aur board exams ke liye bahut important hai.
Step 1: Identify First Term (a) and Common Difference (d)
Given AP:
11, 8, 5, 2, ...
👉 First term (a) = 11
👉 Common difference (d) = 8 – 11 = –3
Step 2: Use nth Term Formula of AP
Formula hota hai:
an = a + (n-1)d
Ab question ke according hume check karna hai ki –150 koi term hai ya nahi.
So, maan lete hain:
an = -150
Formula me values put krte hain:
-150 = 11 + (n-1)(-3)
Step 3: Solve the Equation
Final Conclusion:
Kyuki n ek whole number nahi hai, isliye:
👉 –150 is NOT a term of the given AP.
🎯 Final Answer:
–150 given AP ka term nahi hai.
📌 Exam Writing Tip:
Board exam me hamesha:
First term (a) likho
Common difference (d) nikalo
Formula clearly likho
Proper steps dikhao
Final conclusion box me likho
❓ Frequently Asked Questions (FAQs)
1️⃣ What is the first term and common difference of the AP 11, 8, 5, 2...?
Is AP me first term (a) = 11 hai aur common difference (d) = –3 hai, kyunki har term 3 se decrease ho rahi hai.
2️⃣ What formula is used to check whether a number is a term of an AP?
Hum nth term formula use karte hain:
an = a + (n-1)d
Isi formula se check karte hain ki given number kisi particular value of n par aata hai ya nahi.
3️⃣ Is –150 a term of the AP 11, 8, 5, 2...?
Nahi. Jab hum formula use karte hain to n ki value 164/3 aati hai jo whole number nahi hai.
Isliye –150 given AP ka term nahi hai.
👉 Agar aap AP ke aur bhi similar questions practice karna chahte hain, to is question ka detailed solution bhi dekhein:
Find the number of terms in each of the following APs:18, 15½,13 ......., 47.
