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# Notes on Arithmetic progression

Raj Kumar
23/08/2018 0 0

If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d

The sum, Sn of the first ‘n’ terms of the A.P. is given by Sn = n/2 [2a + (n-1)d]

If Sn is the sum of n terms of an A.P. whose first term is ‘a’ and last term is ‘l’,Sn = (n/2)(a + l)

If common difference is d, number of terms n and the last term l, then Sn = (n/2)[2l-(n -1)d]

If a fixed number is added or subtracted from each term of an A.P.,

then the resulting sequence is also an A.P. and it has the same common

difference as that of the original A.P.

If each term of A.P is multiplied by some constant or divided by a

non-zero fixed constant, the resulting sequence is an A.P. again.

If a1, a2, a3, …, an and b1, b2, b3, …, bn, are in A.P. then a1+b1, a2+b2, a3+b3, ……, an+bn and a1–b1, a2–b2, a3–b3, ……, an–bn will also be in A.P.

Suppose a1, a2, a3, ……, an are in A.P. then an, an–1, ……, a3, a2, a1 will also be in A.P.

If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d

The sum, Sn of the first ‘n’ terms of the A.P. is given by Sn = n/2 [2a + (n-1)d]

If Sn is the sum of n terms of an A.P. whose first term is ‘a’ and last term is L then

Sn = (n/2)(a + L)=n/2(1st term+Last term)

If common difference is d, number of terms n and the last term l,

then Sn = (n/2)[2l-(n -1)d]

If a fixed number is added or subtracted from each term of an A.P.,

then the resulting sequence is also an A.P. and it has the same common

difference as that of the original A.P.

If each term of A.P is multiplied by some constant or divided by a

non-zero fixed constant, the resulting sequence is an A.P. again.

If a1, a2, a3, …, an and b1, b2, b3, …, bn, are in A.P.

then a1+b1, a2+b2, a3+b3, ……, an+bn and a1–b1, a2–b2, a3–b3, ……, an–bn will also be in A.P.

Suppose a1, a2, a3, ……, an are in A.P. then an, an–1, ……, a3, a2, a1 will also be in A.P.

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