Practice Questions on Sequence & Progressions

Arithmetic Progression:

an= a1 + (n-1) * d, where a n is the nth term of A.P, a1 is the first term, d is the common difference.
Sn= [(a1 +an)* n]/2 = [2a1 + (n-1) * d] *n/2, where Sn is sum of first n terms of A.P.
If the common difference is positive, then the progression is an increasing sequence.
If the common difference is negative, then the progression is an decreasing sequence.
If the common difference is 0, then the progression is constant.
Sum of first n natural numbers = n *(n+1)/2 Sum of squares of first n natural numbers = n *(n+1)*(2n+1)/6 Sum of cubes of first n natural numbers = [n *(n+1)/2] ²

Geometric Progression:

an = a1 *r ^n-1 ,a≠0.r≠0 Where an is the nth term a1 is the first term and r is the common ratio.
Sn = [(an*r) -a1]/(r-1) = 11(r ⁿ -1)/(r-1) where Sn is the sum of first n terms of the G.P & r≠1.
If a1 > 0 and r > 1, then the progression is an increasing sequence.
If a1 > 0 and 0 < r < 1, then the progression is an decreasing sequence.
If a1 < 0 and r > 1, then the progression is an decreasing sequence.
If a1 < 0 and 0 < r < 1, then the progression is an increasing sequence.
If r < 0,then irrespective of value of a , the progression alternates its sign and it can be said that the progression neither increases nor decreases.
If r=1, then the progression is constant.

Arithmetic Mean:

Arithmetic mean of 2 numbers a and b = (a+b)/2

Geometic Mean:

Geometic mean of 2 numbers a and b = ab where a > 0 and b > 0
(a+b)/2 ≥ ab, if a > 0 and b > 0