Question

In the sequence 50, 50+k, 50+2k, 50+3k, 50+4k, ….., the 51st term is 350. Then the value of \( k \) is equal to

• A. 6
• B. 8
• C. 10
• D. 15

Answer 1

The Correct Option is A

The general form for the \( n \)-th term of the sequence is: \[ Term_n = 50 + (n-1)k \] For the 51st term, we substitute \( n = 51 \) and set the term equal to 350: \[ 50 + (51 - 1)k = 350 \] \[ 50 + 50k = 350 \] Solve for \( k \): \[ 50k = 350 - 50 = 300 \quad \Rightarrow \quad k = \frac{300}{50} = 6 \] To find the value of \( k \), use the formula for the \( n \)-th term and substitute the known term to solve for \( k \).