Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _____.
Correct Answer: 2223
Solution and Explanation
The correct answer is 2223
Given : 3,6,9,12 ..... upto 78 terms
5,9,13,17 ...... upto 59 terms
Now , last term of first series t78 \(= 3+77×3=234\)
and last term of second series t59 \(= 5+58×4=237\)
Now , common difference of common terms = LCM {3,4} = 12
Therefore , First common term is 9 and last common term is 225
So, series will be 9,21,33 ....... 225
\(∵ t_n = 225\)⇒ 9 + (n-1)12 = 225
⇒ n = 19
∴ Sum of common on terms = \(S_n = \frac{19}{2} (9+225) = 2223\)
Top Questions on Arithmetic Progression
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to
- JEE Main - 2026
- Mathematics
- Arithmetic Progression
- Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to
- JEE Main - 2026
- Mathematics
- Arithmetic Progression
- The vertices B and C of a triangle ABC lie on the line \( \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} \). The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of \( \triangle ABC \) is:
- JEE Main - 2026
- Mathematics
- Arithmetic Progression
- The common difference of the A.P.: \( a_1, a_2, \ldots, a_m \) is 13 more than the common difference of the A.P.: \( b_1, b_2, \ldots, b_n \). If \( b_{31} = -277 \), \( b_{43} = -385 \) and \( a_{78} = 327 \), then \( a_1 \) is equal to:
- JEE Main - 2026
- Mathematics
- Arithmetic Progression
- If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is
- JEE Main - 2026
- Mathematics
- Arithmetic Progression
Questions Asked in JEE Main exam
- If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to
- JEE Main - 2026
- Binomial theorem
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\).
- JEE Main - 2026
- Current electricity
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
- Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are \(2.4 \times 10^8\) m/s and \(2.7 \times 10^8\) m/s, respectively, then the value of critical angle is :
- JEE Main - 2026
- Newtons Laws of Motion
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is:
- JEE Main - 2026
- Thermodynamics
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