Exam Questions & Step-by-Step Markschemes (5 Problems)
Question 1 • 2024
3 Marks
In an Arithmetic Progression (AP), the sum of the first 7 terms is 49 and that of the first 17 terms is 289. Find the sum of the first n terms.
Answer: S_n = n^2
Question 2 • 2024
3 Marks
Find the 20^{\text{th}} term from the last term of the AP: 3, 8, 13, \dots, 253 .
Answer: a_{20}(\text{from end}) = 158
Question 3 • 2024
2 Marks
શાંત સમાંતર શ્રેણી 7, 13, 19, \dots, 205 માં પદોની સંખ્યા શોધો. (Find the number of terms in the AP: 7, 13, 19, ..., 205.)
Answer: n = 34
Question 4 • 2024
4 Marks
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?
Answer: S_{30} = ₹27,750
Question 5 • 2024
3 Marks
If the sum of the first n terms of an AP is given by S_n = 3n^2 + 5n , find the AP and its 15^{\text{th}} term.
Answer: \text{AP: } 8, 14, 20, \dots \quad a_{15} = 92