Question

Sum of the series 3+5+7+6+9+12+9+13+17+.....+3n terms

Answer 1

Answer:

3n (3+2n)

Step-by-step explanation:

We can write this series as

(3+5+7)+(6+9+12)+(9+13+17)+ ………. 3n terms

Now the first series is a collection of the first term of each bracket, the second series is a collection of the second term of each bracket and third series is a collection of the third term of each bracket

= (3+6+9+….. + n terms)+ (5+9+13+….+ n terms)+(7+12+17+…..+ n terms)

So now these are three AP’s

So applying

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

= n/2 [2×3 + (n-1) 3] + n/2 [2×5 + (n-1) 4] + n/2 [2×7 + (n-1) 5]

= n/2 [6+10+14 + (n-1) (3+4+5) ]

= n / 2 [ 30 + 12(n-1) ]

=n/2 [ 18 + 12 n]

=n (9+6n)

= 3n (3+2n)

HOPE THIS HELPS.............