Question

. Find the sum of the given arithmetic series.
The sequence whose general term is an=3n represents the positive multiples of 3. Find the sum of the first 102 positive multiples of 3.

Answer 1

Sum = (n/2)( 2a +(n-1)d )

Answer 2

just about remembering formulas

Answer 3

I dont even need to know what d is ( I could get it by simultaneously eqns ) , because remember that general Tn ( or in your case "an" ) = a +(n-1)d

Answer 4

so the part inside the bracket is:

a+ ( a+(n-1)d )

Answer 5

ok

Answer 6

now I will call "an" T(n) , ie T(n) = 3n

so our sum becomes:

Sum = (n/2) ( a +T(n) )

Answer 7

Now n= 102 ( because we want first 102 terms ) and T(n) = 3n ( thats given to us )

Answer 8

so sum = (n/2) ( a+ 3n )

now we just need to know what "a" is , we already know "n" from before ( its 102 )

so if we sub n=1 into our T(n) formula that will give us the first term ( which is "a" )

so T(1) = a = 3(1) = 3

Answer 9

now sub it in

sum = (102/2) ( 3 + 3(102) ) = 51 ( 309) = 15759

Answer 10

wow i dont know how this comes so easy for u, thank you. i have like 3 more problems ;(