Question:
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Updated On: Nov 3, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
We know that, For an A.P.,
\(a_n = a + (n − 1) d\)
\(a_{17} = a + (17 − 1) d\)
\(a_{17} = a + 16d\) ……. (i)
Similarly,
\(a_{10} = a + (10− 1) d\)
\(a_{10}= a + 9d\) ……. (ii)
It is given that,
\(a_{17} − a_{10} = 7\)
\((a + 16d) − (a + 9d) = 7\)
\(7d = 7\)
\(d = 1\)
Therefore, the common difference is 1.
Was this answer helpful?
0
0
Top Questions on nth Term of an AP
- What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
- JEE Main - 2025
- Mathematics
- nth Term of an AP
Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to
- JEE Main - 2023
- Mathematics
- nth Term of an AP
- Let \(a,b,c>1,a^3,b^3 \text{ and } c^3\) be in A.P., and \(log_ab, log_ca \text{ and } log_bc\) be in G.P. If the sum of first 20 terms of an A.P., whose first term is \(\frac{a+4b+c}{3}\) and the common difference is \(\frac{a−8b+c}{10}\) is −444, then abc is equal to:
- JEE Main - 2023
- Mathematics
- nth Term of an AP
Let $a_1, a_2, a_3, \ldots$ be an AP If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :
- JEE Main - 2023
- Mathematics
- nth Term of an AP
- The $8^{\text {th }}$ common term of the series
$S_1=3+7+11+15+19+\ldots \ldots$
$S_2=1+6+11+16+21+\ldots $ is ______- JEE Main - 2023
- Mathematics
- nth Term of an AP
View More Questions
Questions Asked in CBSE X exam
- The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
- CBSE Class X - 2024
- Quadratic Equations
- The pH of an aqueous solution of a salt is 9. The types of acid and base from which this salt is formed are:
- CBSE Class X - 2024
- Acids, Bases And Salts
- The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
- CBSE Class X - 2024
- Linear Equations
- The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.
- CBSE Class X - 2024
- Coordinate Geometry
- $ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
- CBSE Class X - 2024
- Similarity of Triangles
View More Questions