Quantitative Reasoning

Progression & Series

Medium

If the third and ninth terms of an A.P. are 1 and 19 respectively, then the 23rd term will be:

✅ Correct Option: 2

The 3rd term of an A.P. is 1 and the 9th term is 19.

In an Arithmetic Progression, the nth term is given by:

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

where $a$ is the first term and $d$ is the common difference.

For the 3rd term:

$a_3 = a + 2d$

$a + 2d = 1$ ... (Equation 1)

For the 9th term:

$a_9 = a + 8d$

$a + 8d = 19$ ... (Equation 2)

Subtracting Equation 1 from Equation 2:

$(a + 8d) - (a + 2d) = 19 - 1$

$6d = 18$

$d = 3$

Substituting $d = 3$ into Equation 1:

$a + 2(3) = 1$

$a + 6 = 1$

$a = -5$

The 23rd term is:

$a_{23} = a + 22d$

$a_{23} = -5 + 22(3)$

$a_{23} = -5 + 66$

$a_{23} = 61$

Therefore, the 23rd term is 61.

2025: 19 May Shift 1

If the 5th and 9th terms of an arithmetic progression are 7 and 13, respectively, then the 15th term is:

2025: 15 May Shift 1

If the sum of n terms of an A.P. is $nP + \frac{1}{2}n(n - 1)Q$ , where P and Q are constants, find the common difference.

2025: 16 May Shift 1

The 7th and 9th terms of an arithmetic progression are 10 and 11, respectively. Find the 15th term.

2025: 20 May Shift 1

In an A.P, if $m^{th}$ term is n and the $n^{th}$ term is m, where $m \neq n$ , find the $p^{th}$ term.

2025: 23 May Shift 1

Which of the following list of numbers forms an arithmetic progression?

(A) 1, -1,-3 -5, .......

(B) -1.2, -3.2, -5.2, -7.2, ...........

(D) 2, $\frac{5}{2}$ , 3, $\frac{7}{2}$ ......

Choose the correct answer from the options given below:

2025: 3 June Shift 2

Consider the Arithmetic Progression: 3,8,13,18..... . What is the 18th term of the given Arithmetic Progression.

Choose the correct answer from the options given below:

If the third and ninth terms of an A.P. are 1 and 19 respectively, then the 23rd term will be:

Solution

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