The 3rd and 7th term of an arithmetic progression are 6 and 30 respectively.determine the (i)common difference(ii)first term(iii)10term

(i) d = (30-6)/(7-3) = 6

(ii) a = a3 - 2d = 6 - 12 = -6
(iii) a10 = a7+3d = ____

Did you know?

Did you know that an arithmetic progression is a sequence of numbers where the difference between each consecutive term is constant? By using the given information, we can find various important elements of this sequence. First, the common difference can be determined by subtracting the third term (6) from the seventh term (30) and dividing by the number of terms in between (7 - 3 = 4). This gives us a common difference of 6. Next, we can find the first term by subtracting the common difference multiplied by the position of the third term (3) from the third term itself. In this case, the first term would be 6 - (6 * 2) = -6. Finally, to find the 10th term, we can use the formula: term = first term + (n - 1) * common difference, where n represents the position of the term. Plugging in the values, we get the 10th term as -6 + (10 - 1) * 6 = 48.