kmeds16 Group Title Given a geometric sequence whose sum of the first 10 terms is 4 and whose sum from the 11th to the 30th term is 48, find the sum from the 31st to the 60th term. one year ago one year ago

1. cwrw238 Group Title

Sum of 10 = a * (r^4 - 1) -------- = 4 r- 1

2. kmeds16 Group Title

@cwrw238 why is it r^4? I thought it's r^10.

3. hitten101 Group Title

n is 10 not 4

4. amistre64 Group Title

hmm, given is: $S_n=\frac{1-r^n}{1-r}$ $S_{10}=4=\frac{1-r^{10}}{1-r}$ $S_{30-10}=48=\frac{1-r^{20}}{1-r}$

5. kmeds16 Group Title

@hitten101 yes yes :)

6. shubhamsrg Group Title

you have been given the sum upto first 10 terms =4 you have also been given the sum upto first 30 terms = 4 + 48 =52 and you have 2 eqns with 2 variables ->solve for a and r now calculate sum for first 60 terms from that subtract sum of first 30 terms.. this should help..

7. hitten101 Group Title

|dw:1351514867224:dw|

8. kmeds16 Group Title

a(r^10 - 1) / r - 1 = 4 a(r^30 - 1) / r - 1 = 52 ? @shubhamsrg like this?

9. hitten101 Group Title

solve for a and r.. then find the sum of 60 terms subtract sum of 30 terms from sum of 60 terms

10. shubhamsrg Group Title

@kmeds16 yep @hitten101 mistake in your formulla in the denominator..

11. kmeds16 Group Title

I got, r^10 = 3. this is confusing :/ 10th root of 3?!

12. cwrw238 Group Title

my mistake r^10 not r^4

13. shubhamsrg Group Title

how'd you get that? o.O

14. shubhamsrg Group Title

ahh k..got it

15. hitten101 Group Title

@kmeds16 @shubhamsrg yes no exponent in the denominator.. you are right

16. kmeds16 Group Title

second equation divided by first equation. hehehehehe

17. shubhamsrg Group Title

your main aim is not to find r,, your main aim is to find sum.. leave it as r^10 = 3

18. kmeds16 Group Title

find the sum of S60 and subtract 52, right?

19. shubhamsrg Group Title

seems likely..

20. shubhamsrg Group Title

do this,,this might simplify.. substitue r^10 =3 whereever you can leave r-1 as it is.. you can see a/(r-1) = 4/(r^10 -1) in calculation for sum of 60 terms ,make use of this eqn,, no need to find a.. :)

21. shubhamsrg Group Title

r^60 we all can find.. hmm.. hope that helped..

22. kmeds16 Group Title

solving...hehehe ahm, thanks for the idea..