Question:
In AP, \( a_k=5k+1 \). Find sum of first 100 terms
In AP, \( a_k=5k+1 \). Find sum of first 100 terms
Show Hint
In AP, always find first and last term before applying sum formula.
Updated On: May 1, 2026
- \(50(507)\)
- \(51(506)\)
- \(50(506)\)
- \(51(507)\)
- \(52(506)\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept: Use sum formula of AP:
\[
S_n = \frac{n}{2}(a+l)
\]
Step 1: Find first term: \[ a_1 = 5(1)+1=6 \]
Step 2: Find last term: \[ a_{100} = 5(100)+1=501 \]
Step 3: Substitute values: \[ S = \frac{100}{2}(6+501) \]
Step 4: Simplify: \[ = 50 \times 507 \]
Step 5: Final answer: \[ \boxed{50(507)} \]
Step 1: Find first term: \[ a_1 = 5(1)+1=6 \]
Step 2: Find last term: \[ a_{100} = 5(100)+1=501 \]
Step 3: Substitute values: \[ S = \frac{100}{2}(6+501) \]
Step 4: Simplify: \[ = 50 \times 507 \]
Step 5: Final answer: \[ \boxed{50(507)} \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Sum of First n Terms of an AP Questions
- In an A.P., the first term is 3 and the last term is 17. The sum of all the terms in the sequence is 70. Then the number of terms in the arithmetic sequence is
- The sum of odd integers from 1 to 2001 is
- In AP, \( a_k=5k+1 \). Find sum of first 100 terms
- The sum of odd integers from 1 to 2001 is
- The sum of odd integers from 1 to 2001 is:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions