SCERT Kerala Class 10 Mathematics/ Arithmetic Sequences.

SCERT Kerala Class 10 Mathematics /Arithmetic Sequences is about the practice problems for Class 10 Mathematics Chapter 1 Arithmetic Sequences. Here you can find out extra questions for practice and model questions too.

SCERT Kerala Class 10 Mathematics /Arithmetic Sequences – Chapter 1
Extra Questions for Practice/ Model Questions
Answer the following:

1. Write the sequence of natural numbers which are multiplied by 7 and added to 1. Check whether the sequence is arithmetic sequence or not?
   Solution:
   The sequence is
   7 x 1 + 1 = 8
   7 x 2 + 1 = 15
   7 x 3 + 1 = 22
   7 x 4 + 1 = 29……………
   Here common difference = 15 – 8 = 7, 22 – 15 = 7, 29 – 22 = 7………
   Since the difference between any two consecutive terms is a constant, it is an arithmetic sequence.
2. The algebraic form of an arithmetic sequence is 3n + 2.
   a) What is the arithmetic sequence?
   b) What is the first term?
   c) Write the common difference?
   Solution:
   a)Algebraic form of an arithmetic sequence is 3n + 2
   When n = 1, 3n +2 = 5
   When n = 2, 3n + 2 = 8
   When n = 3, 3n + 2 = 11………………
   So the arithmetic sequence is 5, 8, 11, 14……………….
   b) First term is 5
   c) Common difference = 8-5 = 3
3. Write down an arithmetic sequence with common difference 7. Find its first term and algebraic form of the arithmetic sequence?
   Solution:
   Arithmetic sequence is 7, 14, 21, 28, ——————-
   First term is 7.
   Algebraic form of this sequence is 7n.
4. 4th term of an arithmetic sequence is 17 and 9th term is 37.
   a) What is the common difference?
   b) What is its first term?
   c) Write the arithmetic sequence?
   d) Which term of the sequence is 121?
   Solution:
   a) Common difference = Term difference /Position difference = (37 – 17)/ (9 – 4) = 20/5 = 4
   b) First term = 4th term – 3d = 17 – 3 x 4 = 17 – 12 = 5
   c) Arithmetic sequence is 5, 9, 13, 17, 21……………
   Algebraic form of the sequence is 4n + 1.
   d) n th term = 4n + 1 = 121
   4n = 121- 1 = 120
   n = 120/4 = 30
   So n th term is 121.
5. Find the sum of first 50 natural numbers? Also find 5 + 10 + 15 + 20 + ……………+ 250?
   Solution:
   1 + 2 + 3 + 4 + ———–+ 50 = ½ (50 x 51) = 1275
   5 + 10 + 15 + ———–+ 250 = 5 (1 + 2 + 3 + ——–+ 50) = 5 x 1275 = 6375
6. Consider the arithmetic sequence 5, 8, 11, 14, 17, ————–
   a) Find the common difference?
   b) Write its algebraic form?
   c) Find the 50th term of the sequence?
   d) Find the sum of first 50 terms of the sequence?
   Solution:
   a) Common difference = 8 – 5 = 3
   b) Algebraic form is 3n + 2
   c) 50th term = 3 x 50 + 2 = 150 + 2 = 152
   d) Sum of first 50 terms = 50/2 (5 + 152) = 25 x 157 = 3925
7. The algebraic form of an arithmetic sequence is 7n + 2
   a) Find the first term and common difference?
   b) Find the sum of its first and 10th term?
   Solution:
   a) First term = 7x 1 + 2 = 9
   Second term = 7 x 2 + 2 = 16
   Common difference = 16 – 9 = 7
   b) 10th term = 7 x 10 + 2 = 72
   Sum = 9 + 72 = 81
8. Find the sum of 2 + 4 + 6 + ———-+ 100?
   Solution:
   2 + 4 + 6 + ——– + 100 = 2 (1 + 2 + 3 + ——–+50) = 2 x ½ (50 + 51) = 2550
9. Consider the arithmetic sequence 3, 10, 17, ———–
   a) Find the algebraic form of the sequence?
   b) Find the common difference?
   c) Find the 12th term?
   Solution:
   a) 7n – 4
   b) Common difference = 10 – 3 = 7
   c) 12th term = 7 x 12 – 4 = 84 – 4 = 80
10. Consider the arithmetic sequence 4, 10, 16, ———
    a) What is the common difference of this sequence?
    b) Find the sum of first 5 terms of this sequence?
    c) What is the remainder when each term of the sequence is divisible by 3?
    Solution:
    a) Common difference = 10 – 4 = 6
    b) Sum of first 5 terms = 4 + 10 + 16 + 22 + 28 = 80
    c) 1