Finding the Common Difference - Arithmetic Progressions

$4 \times 8 = 32$

$2 \times 4 = 8$

$\frac{32}{8}$ $= 4 \times 2 = \fbox{8}$

In the above sequence, the first term is $a_1=4\times 2 =8$ and the fourth term is $a_4=4 \times 8 = 32$ . Hence, the common difference can be obtained as follows: $a_4=a_1+3d \implies d=\frac{a_4-a_1}{3}=\frac{32 -8}{3} = 8.$

Information provided by the question : First term : 8 Term = 32 No. of steps from the first term : 4

By explicit formula term = first term + common difference X no. Of steps from initial term. 32 = 8 + d X 4 - 1 32 = 8 + 3 d 32 - 8 = 3 d 24 = 3d 24/3 = d 8 = d. Therefore , the common difference is 8