Quantitative Reasoning

Progression & Series

Medium

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

✅ Correct Option: 2

In an Arithmetic Progression (AP), each term increases or decreases by the same amount called the common difference $d$ .

The formula for any term is:

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

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

The 7th term is 10 and the 9th term is 11.

From the 7th term to the 9th term, there are 2 steps in the sequence.

Change in value $= 11 - 10 = 1$

Number of steps $= 9 - 7 = 2$

Common difference:

$d = \frac{1}{2}$

$d = 0.5$

Using the 7th term to find the first term:

$a_7 = a + (7 - 1)d$

$10 = a + 6(0.5)$

$10 = a + 3$

$a = 7$

Finding the 15th term:

$a_{15} = a + (15 - 1)d$

$a_{15} = 7 + 14(0.5)$

$a_{15} = 7 + 7$

$a_{15} = 14$

Therefore, the 15th term is $14$ .

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:

2025: 2 June Shift 2

Solve the given equation by replacing the question mark "?" with the most appropriate option:

$16^2 + 8^2 - 16 * 8 = \ ?$

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: 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: 22 May Shift 1

In arithmetic progression(A.P.), the first term is 7 and the 6th term is 22. The sum of the first 10 terms of A.P. is:

2025: 29 May Shift 2

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

Solution