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PPT: Arithmetic Progressions
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Page 1
Arithmetic
Progression
Page 2
Arithmetic
Progression
Sequence: A list of numbers
having specific relation
between the consecutive
terms is generally called a
sequence.
e.g. 1, 3, 5, 7,……… (next term
to a term is obtained by
adding 2 with it)
& 2, 6, 18, 54,…….( next term
to a term is obtained by
multiplying 3 with it)
Page 3
Arithmetic
Progression
Sequence: A list of numbers
having specific relation
between the consecutive
terms is generally called a
sequence.
e.g. 1, 3, 5, 7,……… (next term
to a term is obtained by
adding 2 with it)
& 2, 6, 18, 54,…….( next term
to a term is obtained by
multiplying 3 with it)
Arithmetic Progression: If various terms of a
sequence are formed by adding a fixed
number to the previous term or the
difference between two successive
terms is a fixed number, then the sequence
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even
numbers is an example of AP
2) 5, 10, 15, 20, 25…..
In this each term is obtained by adding 5 to
the preceding term except first term.
Page 4
Arithmetic
Progression
Sequence: A list of numbers
having specific relation
between the consecutive
terms is generally called a
sequence.
e.g. 1, 3, 5, 7,……… (next term
to a term is obtained by
adding 2 with it)
& 2, 6, 18, 54,…….( next term
to a term is obtained by
multiplying 3 with it)
Arithmetic Progression: If various terms of a
sequence are formed by adding a fixed
number to the previous term or the
difference between two successive
terms is a fixed number, then the sequence
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even
numbers is an example of AP
2) 5, 10, 15, 20, 25…..
In this each term is obtained by adding 5 to
the preceding term except first term.
Illustrative example for A.P.
=d,where d=1
a a+d a+2d a+3d………………
Page 5
Arithmetic
Progression
Sequence: A list of numbers
having specific relation
between the consecutive
terms is generally called a
sequence.
e.g. 1, 3, 5, 7,……… (next term
to a term is obtained by
adding 2 with it)
& 2, 6, 18, 54,…….( next term
to a term is obtained by
multiplying 3 with it)
Arithmetic Progression: If various terms of a
sequence are formed by adding a fixed
number to the previous term or the
difference between two successive
terms is a fixed number, then the sequence
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even
numbers is an example of AP
2) 5, 10, 15, 20, 25…..
In this each term is obtained by adding 5 to
the preceding term except first term.
Illustrative example for A.P.
=d,where d=1
a a+d a+2d a+3d………………
The general form of an Arithmetic Progression
is
a , a +d , a + 2d , a + 3d ………………, a + (n-
1)d
Where ‘a’ is first term and
‘d’ is called common difference.
Read MoreFAQs on PPT: Arithmetic Progressions
| 1. How do I find the common difference in an arithmetic progression? |  |
Ans. The common difference is the fixed amount between consecutive terms in an arithmetic progression. Subtract any term from the next term: d = a₂ - a₁. For example, in the sequence 2, 5, 8, 11, the common difference is 3. This constant value remains the same throughout the entire AP sequence and is essential for writing the nth term formula and solving progression problems.
| 2. What's the difference between arithmetic progression and geometric progression for CBSE Class 10? | |
Ans. An arithmetic progression has a constant difference between consecutive terms (addition/subtraction pattern), while a geometric progression has a constant ratio (multiplication/division pattern). In AP, terms grow linearly; in GP, they grow exponentially. For example, 3, 6, 9, 12 is AP with d=3, but 2, 6, 18, 54 is GP with ratio 3. Understanding this distinction helps classify sequences correctly in board exams.
| 3. Why am I getting the wrong answer when finding the sum of an arithmetic series? | |
Ans. The most common mistake is confusing the formulas: Sₙ = n/2(2a + (n-1)d) or Sₙ = n/2(first term + last term). Verify which variables you know before selecting a formula. Another frequent error is miscalculating the common difference or the total number of terms. Double-check that n represents the count of terms, not the position value, to avoid calculation mistakes in AP sum problems.
| 4. How do I use the nth term formula to find missing terms in an arithmetic sequence? | |
Ans. The nth term formula is aₙ = a + (n-1)d, where a is the first term, n is the position, and d is the common difference. Substitute known values to find unknowns. If you need the 10th term and know the first term and common difference, plug these directly into the formula. This approach solves real-world AP applications like finding salary increments or population growth over specific time periods.
| 5. Can arithmetic progressions have negative common differences, and how does this affect the sequence? | |
Ans. Yes, arithmetic progressions can have negative common differences, creating decreasing sequences. For instance, 20, 15, 10, 5, 0, -5 has d = -5. The terms decrease by a constant amount rather than increase. The nth term formula aₙ = a + (n-1)d and sum formulas work identically regardless of whether d is positive or negative, making calculations straightforward for descending AP problems.
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