the first four terms in a sequence are 2, 6, 10, 14. what is the nth term? and what is the sum to n terms of the sequence?
the nth term formula is the sum of the first term (a) and the second to last term (n-1) * the common difference (d). so a + (n-1)d where a = 2 and d = 4 in this case is 2 + (n-1)4 = 4n - 2. the sum to n terms is n/2(2a + (n-1)d) and subbing in the correct values we get n/2(22 + (n-1)*4) = n/2(4 + 4n - 4) = 2n^2. thus we know the sum of any value of n terms of this arithmetic series.
JL
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