SCERT Kerala Class 10 Mathematics/ Arithmetic Sequences.

SCERT Kerala Class 10 Mathematics / Arithmetic Sequences is about the extra questions for practice for SSLC students. Here you can find out practice problems/Model questions for the Chapter Arithmetic Sequences.

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

1. Consider the arithmetic sequence 11, 22, 33, ————————
   a) What is its common difference?
   b) Find the algebraic form?
   Solution:
   a) Common difference = 22 – 11 = 11
   b) Here f= 11, d= 11
   Algebraic form is f + (n-1) d = 11 + (n-1)11 = 11 + 11n – 11 = 11n
2. Write the sequence of even numbers greater than 2. Find its algebraic form?
   Solution:
   Sequence of even numbers greater than 2 is 4, 6, 8, 10, —————–
   Algebraic form is f + (n -1) d = 4 + (n-1) 2 = 4 + 2n – 2 = 2n + 2 = 2(n + 1).
3. Is 1917 a term of the sequence 5, 9, 13, ——–?
   Solution:
   Let nth term be 1917.Given f = 5, d = 4
   So dn + f – d = 4n + 5 – 4 = 1917
   4n + 1 = 1917
   4n = 1917 – 1 = 1916
   n = 1916/4 = 479
   Therefore, 1917 is the 479th term.
4. Consider an arithmetic sequence 22/3, 28/3, 34/3, ——————
   a) Find the common difference?
   b) Write the algebraic expression of the sequence?
   c) Is there any counting number in this sequence? Justify your answer?
   Solution:
   a) Common difference = 28/3 – 22/3 = 6/3 = 2
   b) Algebraic expression is f + (n – 1) d = 22/3 + (n – 1) 2
   = 22/3 + 2n – 2
   = 2n + 16/3
   c) Here 2n is a counting number, but if we are adding 16/3 to 2n, it will become a fraction. So there won’t be any counting number in this sequence.
5. Find the 10th term of an arithmetic sequence if its 7th term is 18 and 18th term is 7?
   Solution:
   Given 7th term = 18 and 18th term = 7
   Now 18th – 17th = (18-7) d
   7 – 18 = 11d
   -11 = 11d
   d = 11/ (-11) = -1
   10th term = 7th term + 3d = 18 + 3 (-1) = 18 -3 = 15
6. The algebraic form of an arithmetic sequence is 5n + 2
   a) What is the first term?
   b) Find its common difference?
   c) Write the arithmetic sequence?
   d) What is the remainder when each term is divided by 5?
   Solution:
   a)First term = 5 x 1 + 2 = 7
   b) Common difference = 5
   c) Arithmetic sequence is 7, 12, 17, 22, —————-
   d) When each term is divided by 5, we will get remainder as 2.
7. How many terms are there in the sequence 1, 4, 7, 10, —————– 100?
   Solution:
   n th term = dn + f – d = 100, d = 3, f = 1
   3n + 1 – 3 = 100
   3n – 2 = 100
   3n = 102
   n = 102/3 = 34
   So there are 34 terms in the given sequence.
8. Compute the 25th term of the sequence 19, 28, 37, —————–
   Solution:
   Here common difference = 28 – 19 = 9
   25th term = 1st term + 24d = 19 + 24 x 9 = 235.
9. Write an arithmetic sequence with 3rd term 37 and 7th term 73?
   Solution:
   Given 3rd term = 37, 7th term = 73
   Now 7th term – 3rd term = (7 – 3) d
   73 – 37 = 4d
   36 = 4d
   d = 36/4 = 9
   1st term = 3rd term – 2d = 37 – 2 x 9 = 37 – 18 = 19
   So the required arithmetic sequence is 19, 28, 37, ————-
10. Compute the sum of the first 100 terms of the arithmetic sequence 1, 4, 7, ———?
    Solution:
    100th term = 1st term + 99d = 1 + 99 x 3 = 298
    Now sum of first 100 terms = ½ x 100 x (1 + 298) = 14950.