Find indicated terms?

1) 7th term=32. 3rd term is 20, find 25th term.


2) find the sum of the 75 terms of this arithmetic sequence : 5,2,-1,-4,-7...


3) find the a5th term of the first 30 terms of arithmetic sequence with an explicit rule of an=5n-4


4) find fifth term of (2m-k)^4





how do u do it...i just can't seem to do it %26gt;_%26lt;

Find indicated terms?
1) Assuming an aritmetic sequence





bn = b1 + (n-1)d


letting b3=a1 = 20, then b7=a5 = 32, and b25 = b23


a5 = a1 + (5-1)d


32 = 20 + (5-1)d


32 = 20 + 4d


12 = 4d


3 = d





b25 = a23 = 20 + (23-1)*3


b25 = 20 + 22*3


b25 = 20 + 66


b25 = 86


======================================...


2)


a75 = a1 + (75-1)d; d=-3





a75 = 5 + (75-1)*-3


a75 = 5 + 74*-3


a75 = 5 + -222


a75 = -217





Sn = n/2(a1+an)


S75 = 75/2(5 + -217)


S75 = 75/2(-212)


S75 = -7950


======================================...


3) ????





a5 = 5*5 - 4 = 21


a15 = 5*15 - 4 = 71


a25 = 5*25 - 4 = 121





OR MAYBE





a1 = 5*1 - 4


a1 = 5 - 4


a1 = 1


a30 = 5*30 - 4


a30 = 150 - 4


a30 = 146





Sn = n/2(a1+an)


S30 = 30/2(1 + 146)


S30 = 30/2(147)


S30 = 2205


======================================...


4)





rth term is nCr-1m^n-(r-1)k^r-1





5th term =


4C4m^4-(5-1)k^5-1


4C4 = 1





5th term = k^4
Reply:1) The question is incomplete. What's the type of series? Is it 'arithmetic' or 'geometric' progression? I solved for both:


Arithmetic:(first term=a, the progress factor=q)


n(th) term = a + q*(n-1)


32=a+6q


20=a+2q


So q=3 and a=14 therefore 25th term=14+3*24=86


Geometric:(first term=a, the progress factor=q)


n(th) term = a * q^(n-1)


32=a*q^6


20=a*q^2


So q=(8/5)^(1/4) and a=20/[(8/5)^(1/2)]


You may substitute for 25th term...





2)As per above, here a=5 %26amp; q=-3


In arithmetic progressions, the sum of a series of consequetive terms from 1 to n would be n*[2*a+(n-1)*q]/2


Sum of first 75 terms=75*[2*5+74*(-3)]/2=75*(10-222)/2=-...





3) Your question is meaningless (what's the a5th term?). If you want the sum of the first 30 terms:


a=-4 %26amp; q=5 so sum(30)=30*[2*(-4)+29*5]/2=2055





4) Again your question is wrong. What's the order parameter (m or k)? Once it's cleared, simply substitute 5 instead of it.





Good luck!

wisdom teeth