>
Exams
>
Mathematics
>
Arithmetic Progression
>
the sum of the first 20 terms of an ap is 820 if t
Question:
The sum of the first 20 terms of an AP is 820. If the first term is 5, find the 20th term and the common difference.
Show Hint
Always use the formula \(S_n = \frac{n}{2}[2a + (n - 1)d]\) carefully and simplify each step to avoid errors in solving for \(d\).
CBSE Compartment X - 2025
CBSE Compartment X
Updated On:
Jul 16, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
Step 1: Use the formula for sum of first \(n\) terms of an AP:
\[ S_n = \frac{n}{2}[2a + (n-1)d] \]
Given:
\[ S_{20} = 820, \quad a = 5, \quad n = 20 \]
Step 2: Substitute the values:
\[ 820 = \frac{20}{2}[2(5) + (20 - 1)d]
820 = 10[10 + 19d] \]
Step 3: Solve for \(d\):
\[ 10 + 19d = \frac{820}{10} = 82 \Rightarrow 19d = 72 \Rightarrow d = \frac{72}{19} \]
Step 4: Find the 20th term:
\[ a_{20} = a + 19d = 5 + 19 \cdot \frac{72}{19} = 5 + 72 = \boxed{77} \]
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Arithmetic Progression
Suppose that the number of terms in an A.P. is \( 2k, k \in \mathbb{N} \). If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then \( k \) is equal to:
JEE Main - 2025
Mathematics
Arithmetic Progression
View Solution
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
View Solution
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
View Solution
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
View Solution
22nd term of the A.P.: \(\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) is
CBSE Class X - 2025
Mathematics
Arithmetic Progression
View Solution
View More Questions
Questions Asked in CBSE Compartment X exam
If \( \tan A = \frac{3}{4} \), find \( \sin A \) and \( \sec A \).
CBSE Compartment X - 2025
Trigonometry
View Solution
Find the mean of the following data using the direct method:
CBSE Compartment X - 2025
Mean
View Solution
Find the coordinates of the point which divides the line segment joining A(3, –2) and B(5, 4) in the ratio 2:3.
CBSE Compartment X - 2025
Coordinate Geometry
View Solution
Solve the quadratic equation: \( 2x^2 + 5x - 3 = 0 \)
CBSE Compartment X - 2025
Quadratic Equations
View Solution
Select from the following compounds which is not a base :
CBSE Class X - 2023
CBSE Compartment X - 2023
Acids, Bases And Salts
View Solution
View More Questions