✅ Find the 31st Term of an AP Whose 11th Term is 38 and 16th Term is 73 | Class 10 Maths AP Solution
📘 Chapter: Arithmetic Progression (AP)
📚 Class: 10th Mathematics (NCERT Based)
Aaj hum solve karenge ek important board level question:
🎥 Watch Detailed Video Solution:
Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Yeh question Class 10 Maths – Arithmetic Progression chapter se hai aur exams me frequently poocha jata hai.
🔎 Step 1: Use nth Term Formula
AP ka formula hota hai:
an = a + (n-1)d
Hume diya hai:
a11 = 38
a16 = 73
🔎 Step 2: Formula Apply Karein
11th Term ke liye:
a + 10d = 38. (equation 1)
16th Term ke liye:
a + 15d = 73. (equation 2)
🔎 Step 3: Subtract Equation 1 from Equation 2
🔎 Step 4: Find First Term (a)
Equation 1 me d = 7 put karte hain:
a + 10(7) = 38
a + 70 = 38
a = 38 - 70
a = -32
🔎 Step 5: Find 31st Term
Formula:
a31 = a + 30d
a31 = -32 + 30(7)
a31 = -32 + 210
a31 = 178
🎯 Final Answer:
👉 31st term of the AP is 178.
📝 Exam Writing Tip
Board exam me: ✔ Dono equations clearly likhein
✔ Subtraction properly show karein
✔ d aur a dono find karein
✔ Final answer box me likhein
❓ Frequently Asked Questions (FAQs)
1. How do you find the common difference when two terms are given?
Agar do alag-alag terms di hui ho jaise:
11th term = 38
16th term = 73
Toh dono ko formula me substitute karke do equations banate hain aur subtract karke d (common difference) nikalte hain.
2. What is the common difference in this question?
Is question me calculation ke baad:
Matlab har term 7 se increase ho rahi hai.
👉 Agar aap AP ke aur bhi similar questions practice karna chahte hain, to is question ka detailed solution bhi dekhein:
