Important Formulas: Arithmetic Progression and Geometric Progression | Quantitative for GMAT PDF Download

Formula of Arithmetic Progression

• Formula to find the nth term of an AP is 
• _Tn = a + (n – 1) d 
• where t_n = nth term,
• a= first term ,
• d= common difference,
• n = number of terms in the sequence.

Number of terms in an AP

• Formula to find the numbers of term of an AP is 
  where
  n = number of terms,
  a = first term,
  l = last term,
  d= common difference.

Sum of first n terms in an AP

Formula to find the sum of first n terms of an AP is

where,
a = first term,
d= common difference,
t_n = nth term = a + (n-1)d

Arithmetic Mean

If a, b, c are in AP, then the Arithmetic mean of a and c  is b  i.e.

Some other important formulas of Arithmetic Progression

Sum of first n natural numbers
We derive the formula to find the sum of first n natural numbers

where
S = Sum of first n natural numbers
n = number of First n natural numbers

Sum of squares of first n natural numbers
Formula to find the sum of squares of first n natural numbers is

where
S = Sum of Squares of first n natural numbers
n = number of First n natural numbers.

Sum of first n odd numbers

Formula to Find the Sum of First n odd numbers
S = n²
where
S = Sum of first n odd  numbers
n = number of First n odd numbers.

Sum of first n even numbers
Formula to find the Sum of First n Even numbers is
S = n(n+1)
where
S = Sum of first n Even numbers
n = number of First n Even numbers.

Formulas for GP

Common ratio:
Formula for finding the common ratio

nth term of an GP:

• Formula for finding the nth term of an GP a_n=a₁rⁿ⁻¹ where a₁ = First Term,
  r = common ratio and n = number of Terms

•  
  { if r>1} where, r = common ratio, a₁ = First Term, n = number of terms
• 
   { if r<1} where, r = common ratio, a₁ = First Term, n = number of terms

Sum of an infinite GP :
Formula for Sum of an infinite GP

Geometric Mean (GM) : If two non-zero numbers a and b are in GP, then there GM is GM = (ab)^1/2

If three non-zero numbers a,b and c are in GP, then there GM is GM = (abc)^1/3.