The first and last terms of an AP are 6.7 and 17.1 respectively. If there are 14 terms in the sequence, find its common difference
To find the common difference of the arithmetic progression (AP), we can use the formula:
\[d = \frac{{a_n - a_1}}{{n - 1}}\]
where:
\(d\) = common difference
\(a_n\) = last term of the AP
\(a_1\) = first term of the AP
\(n\) = number of terms in the AP
Given:
\(a_1 = 6.7\)
\(a_n = 17.1\)
\(n = 14\)
Plugging in the values:
\[d = \frac{{17.1 - 6.7}}{{14 - 1}}\]
\[d = \frac{{10.4}}{{13}}\]
\[d ≈ 0.8\]
Therefore, the common difference of the arithmetic progression is 0.8.