Learner Guide : : 17
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lSequence (Progression): A group of numbers
forming a pattern
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lArithmetic Progression (A.P.): A
progression in which each term, except the first,
is obtained by adding a constant to the previous
term. Its terms are denoted by t1, t2, t3,...tn, or
a1, a2, a3, .......an.
A squence is called an arithmetic progression,
if there exists a constant d such that a2 โ a1 = d
, a3 โ a2 = d, a4 โ a3 = d, ..... an +1 โ an = d and
so on. d is called the common difference.
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lFormation of A.P. or General form of A.P.:
If โaโ is the first term and โdโ is the common
difference of an A.P., then A.P. is a, a + d, a +
2d, a + 3d, a + 4d, ....
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lโnโ th term of A.P.: The nth term of the A.P. a,
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ARITHMETIC PROGRESSION
a + d, a + 2d, .... is given by tn = a + (n โ 1) d.
Sometimes nth term is also denoted by an.
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lSum of first n terms of an A.P. : The sum of
first n terms of an A.P. is Sn =
n
2
(a + l), where
l (last term) = a + (n โ 1) d, a = first term,
d = common difference , n = no. of terms
โด sn =
n
2
[2a + (n - 1)d]
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lnth term in terms of sn: If sn is the sum of the
first n terms of an A.P., then the nth term is given
by tn = sn โ sn โ 1.
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lVarious terms of an A.P.: 3 consecutive terms
are a โ d, a, a + d and common difference is d.
4 consecutive terms are a โ 3d, a โ d, a + d, a
+ 3d and common difference is 2 d .
CHECK YOUR PROGRESS:
1. Which of the following progression is an A.P.?
(A) 1, 4, 9, 16 ..... (B) 1, 3, 9, 27 (C) -2, 0, 2, 4, 6, .... (D) 1, 2, 4, 8, ....
2. The common difference of the A.P. 3, 1, -1, -3, .... is
(A) -2 (B) 2 (C) โ3 (D) 3
3. How many two digit numbers are divisible by 3?
(A) 31 (B) 30 (C) 29 (D) 11
4. If the first term and common difference of an A.P are 2 and 4 respectively, then the sum of its first
40 terms is :
(A) 3200 (B) 2800 (C) 1600 (D) 200
5. The sum of the first 10 terms of the A.P. 3, 4, 5, 6, .... is
(A) 65 (B) 75 (C) 85 (D) 110
6. Find the sum of the A.P, 7 + 12 + 17 + 22 + ... +1002.
