# Arithmetic Sequences /SCERT Kerala Mathematics

Arithmetic Sequences – Chapter 1

## SCERT Kerala Syllabus Mathematics Worksheets

1. Consider the arithmetic sequence 3, 8, 13, 18—————
a) Find its common difference?
b) Find its 25th term?
a) Given a = 3
Common difference = 8 – 3 = 5
b) 25th term = a + (n – 1) d = 3 + 24 x 5 = 123
2. 6th term of an arithmetic sequence is 42 and its 10th term is 70.
a) Find the common difference?
b) What is its first term?
a) Common difference = (70 – 42)/ (10 – 6) = 28/4 = 7
b) Given 6th term = 42
6th term = a + 5d = 42
a + 5 x 7 = 42
a + 35 = 42
a = 42 – 35 = 7
3. The algebraic form of an arithmetic sequence is 2n + 3.
a) Find its common difference?
b) What is its first term?
a) When n = 1, 2 x 1 + 3 = 5
When n = 2, 2 x 2 + 3 = 7
When n = 3, 2 x 3 + 3 = 9 ———
Arithmetic sequence is 5, 7, 9, ———-
a) Common difference = 7 – 5 = 2
b) First term = 5
4. Find the following sums:
a) 1 + 2 + 3 + ——- + 20
b) 2 + 4 + 6 + ——– + 20
c) 1 + 3 + 5 + ——– + 20
a) n (n + 1) /2 = (20 x 21)/2 = 210
b) Given a = 2, d = 2
Sum = n/2[2a + (n-1) d] = 20/2 [2 x 2 + (20 – 1)2]
= 10 [4 + 19 x 2]
= 10 [4 + 38] = 10 x 42 = 420
5. Consider an arithmetic sequence of algebraic form 2n + 5
a) Find the common difference?
b) Find its first term?
a) When n = 1, 2n + 5 = 2 x 1 + 5 = 7
When n = 2, 2 x 2 + 5 = 9
When n = 3, 2 x 3 + 5 = 11 ———
So the arithmetic sequence is 7, 9, 11, ———–
a) Common difference = 9 – 7 = 2
b) First term = 7
6. Find the sum of
a) 1 + 2 + 3 + ——- + 200
b) 4 + 8 + 12 + ——— + 800
a) n (n + 1)/2 = (200 x 201)/2 = 20100
b) 4 + 8 + 12 + —— + 800 = 4( 1 + 2 + 3 + —-+ 200)
= 4 x 20100 = 80400
7. Write the algebraic expression for the sequence of natural numbers ending in 1.
Required sequence is 1, 11, 21, 31, ————
1 = 10 x 1 – 9
11 = 10 x 2 – 9
21 = 10 x 3 – 9
Algebraic expression is 10n – 9, for n = 1, 2, 3——————-
8. The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms.
First term = 1
Let the first four terms be f, f+d, f+2d, f+3d.
Given f + f + d + f + 2d + f + 3d = 100
4f +6d = 100 or 2f + 3d = 50
2 + 3d = 50
3d = 48
d = 48/3 = 16
The arithmetic sequence is 1, 17, 33, 49, ————
9. Write four arithmetic sequences with 200 as the sum of the first four terms.
Let the first four terms be x – 3d, x – d, x + d, x + 3d
Given x – 3d + x – d + x + d + x + 3d = 200
4x = 200
x = 200/4 = 50
i) If d = 1, x – 3d = 50 – 3 = 47
x – d = 50 – 1 = 49
x + d = 50 + 1 = 51
x + 3d = 50 + 3 = 53
The arithmetic sequence is 47, 49, 51, 53, ——–
ii) If d = 2, x – 3d = 50 – 6 = 44
x – d = 50 – 2 = 48
x + d = 50 + 2 = 52
x + 3d = 50 + 6 = 56
The arithmetic sequence is 44, 48, 52, 56, ————
iii) If d = 3, x – 3d = 50 – 9 = 41
x – d = 50 – 3 = 47
x + d = 50 + 3 = 53
x + 3d = 50 + 9 = 59
The arithmetic sequence is 41, 47, 53, 59, ——–
iv) If d = 4, x – 3d = 50 – 12 = 38
x – d = 50 – 4 = 46
x + d = 50 + 4 = 54
x + 3d = 50 + 12 = 62
The arithmetic sequence is 38, 46, 54, 62, ———–
10. Find the sum of all three digit numbers which are multiples of 9.