Question

if the sum of first 6 terms is 12 and sum of first 10terms is 60, then find the sum of its n terms.
​

Answer 1

S6=12

Sn=n [ 2a+ (n-1)d]

2

12=6[2a +(6-1)d]

2

12=3[2a+5d]

12/3=2a +5d

4=2a+5d ........... (i)

S10=60

S10=10 [2a+(10-1)d]

2

60=5[2a+9d]

60/5=2a+9d

12=2a+9d ........... (ii)

Subtract (i) from (ii)

12=2a+9d

4 =2a+5d

- - -

8=4d

8/4=d

2=d

put d in (i)

4=2a+5(2)

4=2a+10

4-10=2a

-6=2a

-6/2=a

-3=a

Now,

Sn=n[2×-3+(n-1)(2)]

2

Sn=n[-6+2n-2]

2

Sn=n[-8+2n]

2

Sn= -8n+2n^2

2

Sn=2n(-4+n)

2