Question - Finding the Eighth Term in an Arithmetic Progression

The first term of an arithmetic progression (AP) is given as \( a_1 = 3 \).

The sum of the first and sixth terms is 20. We can express the sixth term as \( a_6 = a_1 + 5d \), where \( d \) is the common difference of the AP.

Therefore, \( a_1 + a_6 = 20 \).

Substitute \( a_1 \) and \( a_6 \) with given values:

\( 3 + (3 + 5d) = 20 \)

Solve for \( d \):

\( 6 + 5d = 20 \)

\( 5d = 14 \)

\( d = \frac{14}{5} \)

Now, find the eighth term \( a_8 \) using \( a_8 = a_1 + 7d \):

\( a_8 = 3 + 7\left(\frac{14}{5}\right) \)

\( a_8 = 3 + \frac{98}{5} \)

\( a_8 = 3 + 19.6 \)

\( a_8 = 22.6 \)