\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.
Solution and Explanation
Top Questions on Arithmetic Progression
- The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
- BITSAT - 2025
- Mathematics
- Arithmetic Progression
- What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?
- BITSAT - 2025
- Mathematics
- Arithmetic Progression
- In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?
- CAT - 2025
- Quantitative Aptitude
- Arithmetic Progression
- The 6th term of the AP \( \sqrt{27}, \sqrt{75}, \sqrt{147}, \ldots \) is:
- CBSE Compartment X - 2025
- Mathematics
- Arithmetic Progression
- Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is:
- JEE Main - 2025
- Mathematics
- Arithmetic Progression
Questions Asked in JEE Main exam
- The electric field of an electromagnetic wave in free space is \[ \vec{E} = 57 \cos \left[7.5 \times 10^6 t - 5 \times 10^{-3} (3x + 4y)\right] \left( 4\hat{i} - 3\hat{j} \right) \, \text{N/C}. \] The associated magnetic field in Tesla is:
- JEE Main - 2025
- Electromagnetic Induction and Inductance
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.In the light of the above statements, choose the correct answer from the options given below:
- JEE Main - 2025
- Current electricity
- Find the equivalent resistance between two ends of the following circuit:
- JEE Main - 2025
- Current electricity
- Find the output voltage in the given circuit.
- JEE Main - 2025
- Current electricity
- A wire of length $ 25 \, \text{m} $ and cross-sectional area $ 5 \, \text{mm}^2 $ having resistivity $ 2 \times 10^{-6} \, \Omega \cdot \text{m} $ is bent into a complete circle. The resistance between diametrically opposite points will be:
- JEE Main - 2025
- Current electricity
Concepts Used:
Arithmetic Progression
Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.
For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.
In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.
For eg:- 4,6,8,10,12,14,16
We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.
Read More: Sum of First N Terms of an AP