Write a recursive formula for the sequence 15, 26, 48, 92, 180, ... Then find the next term.

Question

anonymous · Answer

I know that a1=15. a2-a1=11, a3-a2=22, a4-a3=44, a5-a4=88. I'm not sure how to apply this knowledge to form a formula though.

anonymous · Answer

an - a(n-1) = n 
a1=15 and a= an-1 + n... Would n be 4 and the equation be a=a(n-1)-4?

koikkara · Answer

15+11=26, 26+22=48, 48+44=92, 92+88=180, 180+176=356. By inspection, I saw the pattern of 11, 22, 44, 88 as the numbers added to each to get the next. I figured out the number added was a square times 11, 11*2^0=11, 11*2^1=22, 11*2^2=44, 11*2^3=88, so the next number to add to 180 is 11*2^4=176, which makes the next term 180+176=356

anonymous · Answer

What would my recursive formula be though?

anonymous · Answer

@Koikkara

anonymous · Answer

Would it be a=a(n-1)-4?

koikkara · Answer

a1 = 15, an+1 = an + 2n-1×11

koikkara · Answer

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,

I 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