Algebra questions involve finding the terms in the sequence. When we say that collection of objects is listed in a sequence, we usually means that the collection of objects is ordered in such a way that it is identified as first term, second term and so on.
Example: The amount of money deposited in bank, over several years form a sequence. Sequences have important application in several spheres of human activities. Sequences, following specific patterns are called progressions. Two kinds of progression are Arithmetic progression and Geometric progression.
The Formula for finding nth term of Arithmetic progression
an = a1 + (n-1) d where a1 is the first term
d is the difference
n is the number of term
The Formula for finding nth term of Geometric progression.
Xn = ar(n-1)
a is the first term
r is the difference between 2 terms (common ratio)
Example 1:- General term for Arithmetic sequence is -1, 3, 7,and 11. …. . Find out 14th term.
From the sequence, we have first term a1 = -1
To find the difference d, subtract adjacent terms
Hence we get d = 7-3 =4
Now apply in the formula
an = a1 + (n-1) d
a14 = -1 + (14-1) 4
By calculating we got, a14 = 51
Example 2:- Find out the 10th term of this Geometric sequence 10, 30, 90, 270, 810………..
This sequence has a factor of 3 between 2 numbers
We have value of a = 10
Common ration r =3
Apply the formula
Xn = ar (n-1)
X10 = (10) 3 (10-1)
= 10 3 (9) = 10 * 19683 = 196830 Hence found.