# SOLUTION: write a recursive formula for the sequence 15, 26, 48, 92, 180,... Then find the next term

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 Question 389734: write a recursive formula for the sequence 15, 26, 48, 92, 180,... Then find the next termFound 2 solutions by richard1234, Edwin McCravy:Answer by richard1234(5390)   (Show Source): You can put this solution on YOUR website!Note that the difference between two consecutive terms and is an increasing geometric sequence. In general, we have the sequence: , etc. It is seen that for all . We can substitute p = 11 and r = 2 to obtain , where Since , Note that a recursive sequence is defined on previous terms. It is possible to write each expression in terms of i and other constants, but it wouldn't be recursive. Using the sum of a geometric sequence, we can get Checking, we have , , ,etc. which is the same sequence as the recursion. Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!``` The other tutor found a GENERAL formula, not a RECURSIVE formula. List those in a column beside the numbers n=1 through n=5 n an 1 15 2 26 3 48 4 92 5 180 Out beside each number, write the difference between it and the number just below it. n an 1 15 11 2 26 22 3 48 44 4 92 88 5 180 Observe that those differences are all multiples of 11 n an 1 15 11 = 1×11 2 26 22 = 2×11 3 48 44 = 4×11 4 92 88 = 8×11 5 180 Next we observe that the numbers 1,2,4,8 are these powers of 2: 20,21,22,23 n an 1 15 11 = 1×11 = 20×11 2 26 22 = 2×11 = 21×11 3 48 44 = 4×11 = 22×11 4 92 88 = 8×11 = 23×11 5 180 Finally we observe that the exponents of 2 are 1 less than the values on n in the left-most column, and 1 less than n is n-1. So we think this way : To get the next term an+1 from the previous term an we must add 2n-1×11. So the recursion formula is a1 = 15, an+1 = an + 2n-1×11 So to get the 6th term, a6, from the 5th term, a5, we substitute 5 for n in an+1 = an + 2n-1×11 a5+1 = a5 + 25-1×11 a6 = a5 + 24×11 Now we substitute 180 for a5 a6 = 180 + 24×11 a6 = 180 + 16×11 a6 = 180 + 176 a6 = 356 Edwin```