Question

The sum of the first 11 terms of an arithmetic sequence is 253 and the sum of the next 6 terms is 342. a) What is the 6th term of the sequence? b) What is the 9th term of the sequence? c) What is its common difference? min om less than two times​

Answer 1

Answer:

Sum of first n terms of an arithmetic sequence is 3n

2

+n.

Let a

1

denotes first term of the sequence,

a

2

denotes second term of the sequence,

d denotes common difference of the sequence,

S

n

denotes sum of first n terms of the sequence.

S

n

=3n

2

+n

S

1

=a

1

=3(1)

2

+1=4

S

2

=a

1

+a

2

=3(2)

2

+2=14

∴a

1

+a

2

=14

∴a

1

+a

1

+d=14

∴2a

1

+d=14

∴2(4)+d=14

∴d=6

First term of the sequence is 4 and common difference is 6.