Question

In an arithmetic sequence with common difference 3 in the first 25 terms sum of first 13 terms equal to sum of next 12 terms if what is the difference between 1st term and 14th term​

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.