Which term of the sequence, -9/4, -2, -7/4, is zero.

Correct Answer is : 10th10^{{th}}10th term

Correct Answer is : 10th10^{{th}}10th term

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Sequence and Series

Question : 42 of 86

Marks: +1, -0

\frac{-9}{4}, -2, \frac{-7}{4}, \dots

Solution:

Concept:

Identify the sequence as arithmetic and find the term number where the value is zero.

Explanation:

First term

a = -\frac{9}{4}

Common difference

d = -2 - \left(-\frac{9}{4}\right) = -2 + \frac{9}{4} = \frac{1}{4}

Let the

n^{\text{th}}

term be zero.

Using

a_n = a + (n-1)d

0 = -\frac{9}{4} + (n-1)\cdot\frac{1}{4}

Multiply by 4:

0 = -9 + (n-1)

⇒

n-1 = 9

⇒

n = 10

Thus, the

10^{\text{th}}

term is zero.

Answer:

10^{\text{th}}

term

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