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the 3rd and 7th terms of an arithmetic progression are 6 and 30 respectively. determine the

(I) common difference
(ii) first term
(iii) 10th term

just use your basic formulas....

a+2d=6, a+6d=30
subtract them:
4d=24
d = 6, then mentally ... a = -6
10th term = a+9d
= -6+54
= 48

Did you know?

Did you know that in an arithmetic progression, the common difference is the difference between consecutive terms? In the given progression, the common difference would be found by subtracting the 3rd term (6) from the 7th term (30), which equals 24. Did you know that the first term in an arithmetic progression is found by subtracting the common difference from any given term? To find the first term in this progression, we can subtract the common difference (24) from the 3rd term (6), resulting in -18. Did you know that the n-th term in an arithmetic progression can be found using the formula an = a + (n-1)d, where a is the first term and d is the common difference? To find the 10th term in this progression, we can substitute a = -18, n = 10 and d = 24 into the formula. The 10th term would then be -18 + (10-1) * 24, which equals 210.