Question

the sum of the first n terms of an arithmetic progression is given by n square +5n find the 25th term of the arithmetic progression​

Answer 1

Step-by-step explanation:

When n=1 , S1=a1=6(1)-1^2= 5. …………..[1]

When n=2 , S2=a1+a2=6(2)-2^2=8……...[2]

As we know , a1 =S1=5. …………………….[3]

And S2=a1+ a2.(now put a1=5 as per [3])

We get, 8 =5+a2 => a2=3..………………….[4]

Now, d=a2-a1=3-5=-2.

Formula for a^n term of an A.p. is

=a+(n-1)d

Therefore,

25th term is as follows, ( where n=25)

a25=a+(n-1)d

a25=5+(25-1)(-2)

a25=5+(24)(-2)=-43.

So, 25th term is -43.

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