Example Question - eighth term

Finding the Eighth Term in an Arithmetic Progression

<p>The first term of an arithmetic progression (AP) is given as \( a_1 = 3 \).</p> <p>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.</p> <p>Therefore, \( a_1 + a_6 = 20 \).</p> <p>Substitute \( a_1 \) and \( a_6 \) with given values:</p> <p>\( 3 + (3 + 5d) = 20 \)</p> <p>Solve for \( d \):</p> <p>\( 6 + 5d = 20 \)</p> <p>\( 5d = 14 \)</p> <p>\( d = \frac{14}{5} \)</p> <p>Now, find the eighth term \( a_8 \) using \( a_8 = a_1 + 7d \):</p> <p>\( a_8 = 3 + 7\left(\frac{14}{5}\right) \)</p> <p>\( a_8 = 3 + \frac{98}{5} \)</p> <p>\( a_8 = 3 + 19.6 \)</p> <p>\( a_8 = 22.6 \)</p>