Quantitative Reasoning

Progression & Series

Medium

The 21st and 33rd terms of an arithmetic progression are 91 and 145 respectively. What is the 29th term?

127

130

119

124

✅ Correct Option: 1

An arithmetic progression has the formula:

$a_n = a + (n - 1)d$

Where $a$ is the first term, $n$ is the position, and $d$ is the common difference.

Given that the 21st term is 91 and the 33rd term is 145.

Using the formula for both given terms:

$a_{21} = a + 20d = 91$ ... ①

$a_{33} = a + 32d = 145$ ... ②

Subtracting equation ① from equation ②:

$(a + 32d) - (a + 20d) = 145 - 91$

$12d = 54$

$d = \frac{54}{12}$

$d = 4.5$

Substituting $d = 4.5$ into equation ①:

$a + 20(4.5) = 91$

$a + 90 = 91$

$a = 1$

Finding the 29th term:

$a_{29} = a + (29 - 1)d$

$a_{29} = 1 + 28(4.5)$

$a_{29} = 1 + 126$

$a_{29} = 127$

Therefore, the 29th term is 127.

The answer is option 1.

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The 21st and 33rd terms of an arithmetic progression are 91 and 145 respectively. What is the 29th term?

Solution

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