Arithmetic Progression — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Arithmetic Progression, written for Class 10 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Arithmetic Progression in one look
a list that grows by the same step every time, and the two formulas that follow from it
- A sequence: numbers in a fixed order, each with a position
- Test the gaps: every consecutive difference is the same
- It is an A.P.: first term and common difference describe it fully
The definition, stated carefully
- a sequence is an A.P. when the difference between any term and the one before it is constant
- that constant is the common difference d, and d = t_2 - t_1 = t_3 - t_2 and so on
- d is found by later term minus earlier term, never the other way round
- d may be positive, giving a rising list, negative, giving a falling one, or zero, giving a constant list
- checking one pair of terms is not enough. A list is an A.P. only if every consecutive difference agrees
The formulas this chapter is built on
- the n-th term, counting from the first
t_n = a + (n-1)d - sum of the first n terms
S_n = n/2[2a + (n-1)d] - the same sum when the last term is known
S_n = n/2(a + t_n) - recovering a single term from the sums
t_n = S_n - S_n-1 - sum of the first n natural numbers
S_n = n(n+1)/2
Why the n-th term has n minus 1 in it
- the first term has had no step added to it yet, so t_1 = a
- the second term has had one step added, t_2 = a + d, and the third has had two
- so the term at position n has had (n-1) steps, giving t_n = a + (n-1)d
- this is the single most useful sanity check in the chapter: substitute n = 1 and the formula must return a
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Arithmetic Progression sheet covers
- A sequence
- Test the gaps
- It is an A.P.
- Arithmetic progression
- Common difference
- The definition, stated carefully
- The formulas this chapter is built on
- the n-th term, counting from the first
- sum of the first n terms
- the same sum when the last term is known
- recovering a single term from the sums
- sum of the first n natural numbers
- Why the n-th term has n minus 1 in it
- Finding which term a given number is
- A sum where the number of terms is unknown
- Terms in A.P.
- Selection of terms
- Choosing terms cleverly when the sum is given
- Using the symmetric choice
- Word problems that are A.P.s in disguise
- Which formula does the question want
- Use tn
- Use Sn
- Symbols in this chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Arithmetic Progression the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.