Sequences & Series

Question 1

A sequence in which every term is created by adding or subtracting a definite number to the preceding number

Answer 1

Arithmetic Sequences

Question 2

A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number

Answer 2

Geometric Sequences

Question 3

Each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fn = Fn-1 + Fn-2

Answer 3

Fibonacci Numbers

Question 4

The nth term of the geometric sequence is given by

Answer 4

ar^(n-1)

Question 5

General form of an AP

Answer 5

a + (n-1)d

Question 6

General form of a GP

Answer 6

a, ar, ar²
when sum/product is given, a/r, a, ar

Question 7

Sum of first n terms of a GP

Answer 7

S_n = a(1 – rⁿ)/(1 – r) if |r| < 1
S_n = a(rⁿ-1)/(r – 1) if |r| > 1
S_n = a/(1-r) if r=∞

Question 8

Sum of first n terms of an AP

Answer 8

S_n = n/2(2a+(n-1)d)

Question 9

Geometric mean

Answer 9

b=√ac

Question 10

Arithmetic mean

Answer 10

b=(a+c)/2

Question 11

Relation b/w AM & GM

Answer 11

AM ≥ GM
(√a+√b)²/2≥0

Question 12

Take a point for fun

Answer 12

:)