Ex 5.2 Q18 - The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Solution:-Let,
First term = a
Common difference = d
*nth term of an AP is given by,
aₙ = a + (n - 1)d
Case (i): The sum of 4th and 8th term of the AP is 24,
∴ a₄ + a₈ = 24
∴ a + 3d + a + 7d = 24
∴ 2a + 10d = 24
*Taking 2 as common,
∴ a + 5d = 12
∴ a = 12 - 5d ------- (i)
Case (ii): The sum of 6th and 10th term of the AP is 44,
∴ a₆ + a₁₀ = 44
∴ a + 5d + a + 9d = 44
∴ 2a + 14d = 44
*Taking 2 as common,
∴ a + 7d = 22
∴ 12 - 5d + 7d = 22
∴ 7d - 5d = 22 - 12
∴ 2d = 10
∴ d =
10
/
2
∴ d = 5
➙ Putting d = 5 in Eqⁿ(i)
∴ a = 12 - 5(5)
∴ a = 12 - 25
∴ a = -13
Now,
*First term, a
= a
= -13
*Second term, a₂
= a + d
= -13 + 5
= -8
*Third term, a₃
= a + 2d
= -13 + 2(5)
= -13 + 10
= -3
Hence,
The first three terms of the AP are -13, -8 and -3.
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Try This..
✒ The sum of the 5th and 9th terms of an AP is 52. Find its first term and common difference.
✒ If the 3rd and 7th terms of an AP are 9 and 25 respectively, find the AP.
✒ Find the 10th term of an AP whose first term is 2 and the common difference is 3.
❌ Common Mistakes
Forgetting the formula aₙ = a + (n - 1)d:▸ Always start from the basics.Mixing up term numbers and values:▸ Remember, aₙ is a value; n is just the position.Arithmetic errors in solving equations:▸ Double-check your addition and subtraction.Not substituting correctly:▸ After finding one variable, plug it back carefully.
📝 Related Questions:-
- Ex 5.2 Q16 - Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
- Ex 5.2 Q17 - Find the 20th term from the last term of the AP: 3, 8, 13, ... , 253.
- Ex 5.2 Q19 - Subba Rao started work in 1995 at an annual salary of ₹5000 and received an increment of ₹200 each year. In which year did his income reach ₹7000?
- Ex 5.2 Q20 - Ramkali saved ₹5 in the first week of a year and then increased her weekly savings by ₹1.75. If in the nth week, her weekly savings become ₹20.75, find n.
Queries Solved:-
Class 10 Ex 5.2
Ex 5.2 Q18 Class 10
Class 10 Ex 5.2 Q18
Class 10 Chap 5 Ex 5.2 Q18
Class 10 Arithmetic Progression
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