Question

Write the first term of the arithmetic sequence 1, 25, 49, 73, 97,….

b) How many perfect square terms are in the arithmetic sequence 97, 73, 49,…

[2 marks]

II.

Read the following passage. Understand the mathematical concept in it and

answer the questions that follow. Each question carries 1 score. [6 * 1 = 6]

The common difference of the arithmetic sequence 15, 14, 13, 12, 11, 10 ….. is 14

– 15 = -1. The first term of the sequence is 15 and the 15th term is 15 + (14 × -1) =

15 – 14 = 1. Similarly, the 4th term is 12 and the 12th term is 4. Its 16th term is

x16 = 15 + (15 × -1) = 15 – 15 = 0. So, the sum of the first 31 terms is also 0. That

is if the nth term of an arithmetic sequence with common difference -1 is m, then

the mth term is n and the (m + n)th term is 0.

[a] 7th term of an arithmetic sequence is 10 and the 10th term is 7. What is the

common difference?

[b] What is the 21st term of the arithmetic sequence 21, 20, 19….

[c] 5th term of an arithmetic sequence is 17 and the 17th term is 5. Which term of

the sequence is 0?

[d] 5th term of an arithmetic sequence is 17 and the 17th term is 5. What is the

44th term?

[e] 1st term of an arithmetic sequence is n and the nth term is 1. What is the (n +

1)th term?

[f] The 1st term of an arithmetic sequence is n and the nth term is 1. Sum of how

many terms, starting from the first term, of this sequence is 0?

[ 6 marks]

III. [a] Write the first integer term of the arithmetic sequence (1 / 7), (2 / 7),

(3 / 7) …….

[b] What is the sum of the first 7 terms of the above sequence?

[2 marks]

IV. If the terms of the arithmetic sequence (2 / 9), (3 / 9), (4 / 9), (5 / 9), ……. are

represented as x1, x2, …. then

[a] x1 + x2 + x3 =

[b] x4 + x5 + x6 =

[c] Find the sum of the first 9 terms.

[d] What is the sum of the first 300 terms?

[5 marks]

​

Answer 1

Answer:

(d) 45150

............