Write a recursive formula for the sequence formula 15,26,48,92,180,.. then find the next term.
can someone please help me
Look like Tn = 2T(n-1) - 4
26 = 2*15-4
48 = 2*26-4
so, what's 2*180-4?
got it thanks
To find the recursive formula for the given sequence, we need to identify the pattern between consecutive terms. Let's analyze the differences between consecutive terms:
26 - 15 = 11
48 - 26 = 22
92 - 48 = 44
180 - 92 = 88
We can observe that each difference is double the previous difference. Hence, the recursive formula for the sequence can be written as follows:
a(1) = 15
a(n) = 2 * a(n-1) + (n-1)
To find the next term in the sequence, we need to substitute the value of n with 6 (since there are already 5 terms given):
a(6) = 2 * a(5) + (6-1)
= 2 * 180 + 5
= 360 + 5
= 365
Therefore, the next term in the sequence is 365.
To find the recursive formula for the given sequence, we need to identify the pattern between consecutive terms. Looking at the sequence, we can observe that each term is obtained by multiplying the previous term by a number and then adding a constant. Let's determine this pattern step by step:
1st term: 15
2nd term: (15 × 1) + 11 = 26
3rd term: (26 × 1) + 22 = 48
4th term: (48 × 1) + 44 = 92
5th term: (92 × 1) + 88 = 180
From the pattern analysis, we can deduce that the recursive formula for the sequence is:
a(1) = 15 (First term)
a(n) = (a(n-1) × 1) + (a(n-1) - 4) (for n > 1)
Now, to find the next term, we substitute n = 6 into the recursive formula:
a(6) = (a(6-1) × 1) + (a(6-1) - 4)
= (a(5) × 1) + (a(5) - 4)
= (180 × 1) + (180 - 4)
= 180 + 176
= 356
Therefore, the next term in the sequence is 356.