Quantitative Reasoning

Progression & Series

Medium

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

✅ Correct Option: 1

For any term in an arithmetic progression:

$n$ th term $= a + (n - 1)d$

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

Given that the 5th term is 7:

$a + (5 - 1)d = 7$

$a + 4d = 7$ -----(Equation 1)

Given that the 9th term is 13:

$a + (9 - 1)d = 13$

$a + 8d = 13$ -----(Equation 2)

Subtracting Equation 1 from Equation 2:

$(a + 8d) - (a + 4d) = 13 - 7$

$a + 8d - a - 4d = 6$

$4d = 6$

$d = \dfrac{6}{4}$

$d = 1.5$

Substituting $d = 1.5$ into Equation 1:

$a + 4(1.5) = 7$

$a + 6 = 7$

$a = 1$

The 15th term is:

$a + (15 - 1)d$

$= 1 + 14(1.5)$

$= 1 + 21$

$= 22$

Therefore, the 15th term is 22.

2025: 27 May Shift 1

The sum of n terms of the series

$1 + \frac{3}{2} + 2 + \frac{5}{2} + 3 + \frac{7}{2} + ...$

2025: 16 May Shift 1

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

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:

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: 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: 13 May Shift 2

If each term of a geometric progression (GP) is positive and is the sum of two preceding terms, then the common ratio of the GP is:

Solution