## anonymous 5 years ago How do I find the twelfth term of 5,8,11,14

1. anonymous

That's an arithmetic progression. The formula for the nth term of an arithmetic progression is:$u _{n}=a+(n-1)d$Where a is the first term and d is common difference. So, to find the twelfth term of this sequence:$u _{12}=a+(12-1)d=5+11\times3=38$

2. amistre64

3. amistre64

A{n} = A{n-1} +3

4. anonymous

That's the recurrence relation but that's not particularly necessary here.

5. amistre64

i dont operate on necessary lol

6. anonymous

Ok thank you

7. anonymous

its 3n + 2 :D( n = term) for n = 1(first term): 3 + 2 =5 for n= 2(second term): 6 + 2 = 8 for n=20(20th term) 60 + 2 = 62 kk?

8. anonymous

just they way i solve is really easier

9. amistre64

$$A_n = A_{n-1}+3$$; and $$A_{n-1} = A_{n-2}+3$$ $A_n = A_{n-2}+3+3 \iff A_n=A_{n-2}+2(3)$ $A_n = A_{n-r} + r(3)$ $$A_{n-r} = A_1;$$ when $$r = n-1$$  $$A_n = A_1 + (n-1)(3);$$ and $$A_1 = 5$$ $A_{12} = 5 + (12-1)(3) = 38$ Thats how you learn it in discrete math ...

10. anonymous

97 to go and then i open a bottle of champagne!

11. amistre64

97..years? or seonds lol

12. anonymous

if it happens when i am not here i will be sad

13. amistre64

ill send a carrier pigeon just before it happens to let you know lol