Ex 5.3 Q6 - The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Solution:-Given,
First term = a₁ = 17
Last term = aₙ = 350
Comman difference = d = 9
What to find?
1. No. of terms in AP
2. Sum of AP
➙ We know that,
aₙ = a + (n - 1) d
∴ 350 = 17 + (n - 1) 9
∴ 350 = 17 + 9n - 9
∴ 350 - 17 + 9 = 9n
∴ 342 = 9n
∴ n =
342
/
9
∴ n = 38
Therefore, There are 38 terms in the AP.
➙ We know that,
Sₙ =
n
/
2
(a + aₙ) ∴ S₃₈ =
38
/
2
(17 + 350) ∴ S₃₈ = 19 (367)
∴ S₃₈ = 6973
Therefore, The sum of AP is 6973.
Hence,
There are 38 terms in the AP and their sum is 6973.
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Try This..
✒ If the sum of the first n terms of an AP is 740, the first term is 20 and the last term is 100, find the number of terms.
✒ In an AP, the first and last terms are 10 and 100. The number of terms is 10. Find the common difference and the sum.
✒ The first term of an AP is 5 and the common difference is 3. If the last term is 50, find the number of terms and their sum.
❌ Common Mistakes
Mixing up formulas:▸ Always double-check whether you’re using the nth term or sum formula.Incorrect subtraction or division:▸ Small calculation errors can throw off your entire answer.Forgetting to add 1 in (n - 1):▸ This is the most common mistake!Using the wrong value for the last term:▸ Ensure that "last term" matches the formula properly.
📝 Related Questions:-
- Ex 5.3 Q4 - How many terms of the AP: 9, 17, 25,... must be taken to give a sum of 636?
- Ex 5.3 Q5 - The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
- Ex 5.3 Q15 - A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹200 for the first day, ₹250 for the second day, ₹300 for the third day, etc., the penalty for each succeeding day being ₹50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
- Ex 5.3 Q16 - A sum of ₹700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹20 less than its preceding prize, find the value of each of the prizes.
- Ex 5.3 Q17 - In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Queries Solved:-
Class 10 Ex 5.3
Ex 5.3 Q6 Class 10
Class 10 Ex 5.3 Q6
Class 10 Chap 5 Ex 5.3 Q6
Class 10 Arithmetic Progression
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