Sequence Value

Arithmetic involves the rules for primary operations that are applicable to whole numbers, integers, rational and irrational numbers, in a single word, to all the real numbers. Arithmetic deals with properties of the counting numbers and fractions and the manipulation of numbers using four kinds of operations such as addition, subtraction, multiplication, and division. Sequence is used for findig the next term in the series or arranging the group of items in particular order.


Looking out for more help on Finite Sequence in algebra by visiting listed websites.

Example Problems on Sequence Value:

Pro 1: Find the sum of all positive integers, from 14 to 2534 inclusive, which are divisible by 14.

Sol :  Sequence value of first few elements of positive integers divisible by 14 are given by 14, 28, 42...

The above sequence value has a first element equal to 14 and a common difference d = 14. We need to know the rank of the term 2534. We use the following formula for the nth term

an = a1 + (n - 1)d

2534 = a1 + (n - 1)d

Substitute value of a1 and value of d by their values

2534 = 14 + 14(n - 1)

Solve for n to obtain

n = 181

2534 is the value of 181st term, we can use the following formula to find sum

sn = n (a1 + an) / 2

s181 = 181 (14 + 2534) / 2 = 230594

Pro 2 : Find the sum of the first 36 positive integers divisible by 9.

Sol :   The sequence of the first 36 positive integers divisible by 9 is given by 9, 18, 27…

The above sequence has a first term equal to 9 and a common difference d = 9. The nth

term formula to find the value of 36th term is

an = a1 + (n - 1 )d

a36 = 9 + 9 (36 - 1) = 324

Now we know the value of first term and value of last term so we can find the sum of the first 36 terms using the following formula

sn = n (a1+ an) / 2

s36 = 36 (9 + 324) / 2 = 5994

Algebra is widely used in day to day activities watch out for my forthcoming posts on Terminating Decimals and How to Calculate Molar Mass. I am sure they will be helpful.

Problems for Practice on Sequence

Pro 1: Find the sequence value of a28 given that a3 = 12 and a12 = 48

Ans : a28 = 112

Pro 2: Find the sequence value of a21 given that the first few terms of an arithmetic sequence are given by 3, 6, 9...

Ans :  a21 = 63