Question

If a_{n} = i ^ ((n + 1) ^ 2) ,neN then the value of a 1 +a 3 +a 5 + - - - - a_{25} is (a) 13 (b) 15 (c) 17 (d) N.O.T.

Answer 1

Answer:

We know that sum of n terms of an A.P. is given by

S

k

=

2

k

{2a

1

+(k−1)d}

So,

S

n

S

m

=

S

n

S

5n

=

2

n

{6+(n−1)d}

2

5n

{6+(5n−1)d}

=

n{6+(n−1)d}

5n{6+(5n−1)d}

=

{(6−d)+n}

5{(6−d)+5nd}

Since,

S

n

S

m

is independent of n , so d=6.

If d=6 then a

2

=a

1

+d=3+6=9