The 6th and 17th terms of an A.P. are 19 and 41 respectively. Find the 40th term

Step 1 (Set up Equations): In an Arithmetic Progression (A.P.), the $n$-th term is given by the formula $a_n=a+(n-1)d$, where $a$ is the first term and $d$ is the common difference.

• The 6th term is 19:

• The 17th term is 41:

Step 2 (Solve for d and a): Subtract Equation 1 from Equation 2:

Substitute $d=2$ back into Equation 1:

Step 3 (Find the 40th term): Using the values $a=9$ and $d=2$, we compute $a_{40}$:

Step 4 (Conclusion): The 40th term of the A.P. is exactly 87.