as sequence help please

[tanmaydube]

q1) The r th term of an arithmetic progression is 1+4r. Find, in terms of n, the sum of the first n terms of the progression.(Ans: n(2n+3) )
q2)The sum of the first twenty terms of an arithmetic progression is 50 , and the sum of the next twenty terms is -50. Find the sum of the first hundred terms of the progression.( Ans: -750)
q3) An arithmetic progression has first term a and common difference -1. The sum of the first n terms is equal to the sum of the first 3n terms. Express a in terms of n. (Ans : 2n-1/2)

Guys please help!
Little help is also appreciated.

THANK YOU!

 

[mrpaudel]

q1) rth term=1+4r...(r+1)th term=1+4(r+1)....now d=(r+1)th term- rth term= 4

rth term=1-4r
or, a+(r-1)d=1+4r
or, a+(r-1)4=1+4r
or,a=5

now....sum of n terms = n/2 {2a+(n-1)d}
out a=5 and d=4 and solve it

q2) for sum=50
n/2{2a+(n-1)d}=50 and put n=20 to get 2a+19d=5--------------(1)

for sum=-50
n/2{2A+(n-1)d}=-50 ( the first term for this one is 21st term from the 1st...so since we wrote a for the first term of whole A.P, we cannot write a..so instead A there....and..A=a+20d...since that A is 21st term )
so...
n/2{2(a+20d)+(n-1)d}=-50..put n=20 to get 2a+59d= -5-------------(2)

solve two equations to get a=39/8 and d=-1/4

now get the sum upto hundred as -750

 

[mrpaudel]

q3) n/2 {2a+1-n} = 3n/2 {2a+1-3n} to give a=4n-1/2 idk if its correct..since this one didnt match to ur answer.....!!

 

[sweetiepie]

some tips for sequence

viewtopic.php?f=24&t=2842&p=52209&hilit=sequence#p52209
viewtopic.php?f=24&t=825&hilit=sequences

i hope it helps