Sample Problems on Arithmetic Sequence
Problem 1: Write the first three terms in each of the following sequences defined by
- An=5n+2(n-1)
- An=2n +4(n-2)
Solution :
For An=5n+2(n-1)
Put n=1, we get
a1=5.1 + 2(1-1) = 5+ 0 =5
Put n=2, we get
a2=5.2+2(2-1) =10+2 =12
Put n=3, we get
a3=5.3 + 2(3-1) =15 + 4 =19
So first three terms are 5,12, 19.
For An=2n +4(n-2)
Put n=1, we get
a1=2.1+4(1-2) =2-4 = -2
Put n=2, we get
a2 = 2.2+4(2-2) =4+ 0 =4
Put n=3,we get
a3= 2.3 + 4(3-2) =6+4 =10
So the first three terms are -2, 4, 10.
Problem 2: Find the 20th Term of the given expression An=(n-1)(2-n)(3+n).
Solution:
For An=(n-1)(2-n)(3+n)
Put n=20 in given expression,
a20 =(20-1)(2-20)(20+3)
⇒ a20 = 19×(-18)×(23)
⇒ a20 = -7886.
Problem 3: Find the sum of all natural numbers lying between 100 and 1000 (inclusive of both 100 and 1000) which are multiples of 5.
Solution:
Solve: first term to be 100 and last terms is 1000 and common difference is 5.
So our formula is Sn=(n/2)[2a+(n-1)×d] .
using an = a1 + (n-1)d
⇒ 1000 = 100 + (n – 1)5
⇒ 900 = (n – 1)5
⇒ 180 = n – 1
⇒ n = 181
Thus, there are 181 such number. Now for sum of all the 181 terms of sequence can be calculated as follows:
S181 = (181/2)[2·100 +(181-1)×5].
⇒ S181 = (181/2)[200+180×5]
⇒ S181 = (181/2)×1100
⇒ S181 = 181×550 = 99,550
Arithmetic Sequence
Arithmetic Sequence is a type of sequence out of all sequences where each term of the sequence is related to the previous term of the sequence by a linear relation. A sequence is a collection of objects where all the terms follow an order or pattern by which the whole sequence can be identified. In the case of an Arithmetic Sequence, each term can be found by adding a constant to the preceding term of the Arithmetic Sequence, this constant sets the Arithmetic Sequence apart from the other sequences.
In this article, we will explore the concept of Arithmetic Sequence and various formulas associated with it. We will also learn about the various properties of Arithmetic Sequences.
Table of Content
- What is Arithmetic Sequence?
- Arithmetic Sequence Definition
- Arithmetic Sequence Examples
- Arithmetic Sequence Formula
- Nth Term of Arithmetic Sequence
- Recursive Formula for Arithmetic Sequence
- Sum of terms in Arithmetic Sequence
- Arithmetic Series
- Properties of Arithmetic Sequence
- Arithmetic Sequence and Geometric Sequence
- Sample Problems on Arithmetic Sequence
- Arithmetic Sequence Worksheet