## anonymous 5 years ago write the following sequence in an form and find the value of the 15th term 4,9,14,19. What is the sum of the first 15 terms of the above sequence?

1. mathteacher1729

Opening question: What is the pattern in this sequence? In other words, how do we get the next term, and the next, and the next...

2. anonymous

add 5 would the equation be an=-1 + 5n?

3. anonymous

it is an arithmatic progresion.series.... a = 4, d= 5, n=15 sum of 15 terms S15= n/2[ 2a +(n-1)d] = 15/2[ 8+14*5] = 15/2[78] = 15*39 = 585

4. anonymous

the formula for sum is s of n= n(a sub 1 + a sub n) divided by 2

5. anonymous

15 th term = a+(n-1)d = 4 + 14*4 =60

6. anonymous

i got 59..

7. anonymous

sorry, it is 4 + 14*5 = 74

8. anonymous

ok and what is the equation of the sequence in a sub n form

9. anonymous

do you have aim?

10. anonymous

already written......... a = first term d= common difference n= number of terms

11. anonymous

no it has to be like an=-1+5n is that right?

12. anonymous

for nth term a+(n-1)d for sum of first n terms n/2[2a +(n-1)d]

13. anonymous

yeah iknow but you plug in a as 4 and d as 5 and simplify what you can i thought?

14. anonymous

if you have problem to understand it , you r welcome to talk to me using skype, i m unable to explain it.......... skype id : sudhanshu_kmr

15. anonymous

do you have instant messenger?

16. anonymous

no......

17. anonymous

ok another question for you:$\sum_{n=1}^{3}i^n-1$

18. anonymous

its i to the n-1 power

19. anonymous

i +i^2 +i^3 -1 = i -1 - i -1= -2 as i^2 = -1, i^3 = -i

20. anonymous

i ended up with an answer of i?