Question

in an ap which certain 100 terms if a10 + a91 = 2 then a40 + a61 = ?

Answer 1

Answer:

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

S

k

=

2

k

{2a+(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

Answer 2

Answer:

2

Step-by-step explanation:

a10+a91=a+9d+a+90d

            =2a+99d

a40+a61=a+39d+a+60d

             =2a+99d

∴a40+a61=2

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