Question

Sum of the first 11terms of an A.S is 275 and the sum of the next 6terms is 354
1.what is the 6th term?
2.what is the 9th term?
3.write the nth term of the sequence.
4.write the sum to n terms of the sequence

Answer 1

Answer:

(I)T6=25

(ii)T9=37

(III)Tn=1+4n

(iv)Sn=2n^2+3n

Step-by-step explanation:

S11=275

S11=11/2 {2a + 10d}

275=11(a+5d)

25=a+5d

a=25-5d ---------------eq 1

acco. to question

S17-S11=354

354={17/2 (2a + 16d)} - 275

629=17(a+8d)

37=a+8d

Now, from eq1 a=25-5d

37=25-5d+8d

12=3d

d=4

therefore a=25-5(4)

a=5

T6=a+5d

T6=5+20

T6=25

T9=a+8d

T9=5+8(4)

T9=37

Tn=a+(n-1)d

Tn=5+(n-1)4

Tn=5+4n-4

Tn=1+4n

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

Sn=n/2{10+(n-1)4}

Sn=n(5+(n-1)2}

Sn=n(5+2n-2)

Sn=n(3+2n)

Sn=2n^2+3n