Question

the first term of an arithmetic progression is -3. if the sixth term is 22, find the mean of the common difference and the first term.

Explanation:

Step1: Recall arithmetic sequence formula

$a_n = a_1 + (n-1)d$
Given $a_1=-3$, $a_6=22$, $n=6$.

Step2: Calculate common difference $d$

Substitute values into formula:
$22 = -3 + (6-1)d$
$22 + 3 = 5d$
$25 = 5d$
$d=5$

Step3: Compute mean of $d$ and $a_1$

Mean = $\frac{d + a_1}{2} = \frac{5 + (-3)}{2} = \frac{2}{2}=1$

Answer:

1