Q: Find the 10th term of the Arithmetic Progression: 2, 7, 12, ...

Given Arithmetic Progression: 2, 7, 12, ... \nStep 1: Identify the first term ($a$) and the common difference ($d$).\nThe first term $a = 2$.\nThe common difference $d = a2 - a1 = 7 - 2 = 5$. \nStep 2: Recall the formula for the $n$-th term of an AP. $an = a + (n - 1)d$ \nStep 3: Substitute the give

Q: Find the sum of the first 22 terms of the AP: 8, 3, -2, ...

Given AP: 8, 3, -2, ... \nStep 1: Identify the first term ($a$), common difference ($d$), and number of terms ($n$).\nFirst term, $a = 8$\nCommon difference, $d = 3 - 8 = -5$\nNumber of terms, $n = 22$ \nStep 2: Recall the formula for the sum of the first $n$ terms of an AP. $Sn = \frac{n}{2} 2a + (

Q: Check whether 301 is a term of the list of numbers 5, 11, 17, 23, ...

Given list of numbers: 5, 11, 17, 23, ... \nStep 1: Check if the sequence forms an AP. $11 - 5 = 6$ $17 - 11 = 6$ $23 - 17 = 6$\nSince the difference between consecutive terms is constant ($d = 6$), the given list is an AP with first term $a = 5$ and common difference $d = 6$. \nStep 2: Assume that

Question 1

Find the 10th term of the Arithmetic Progression: 2, 7, 12, ...

Accepted Answer

Given Arithmetic Progression: 2, 7, 12, ... 
Step 1: Identify the first term ($a$) and the common difference ($d$).
The first term $a = 2$.
The common difference $d = a2 - a1 = 7 - 2 = 5$. 
Step 2: Recall the formula for the $n$-th term of an AP. $an = a + (n - 1)d$ 
Step 3: Substitute the give

Question 2

Find the sum of the first 22 terms of the AP: 8, 3, -2, ...

Accepted Answer

Given AP: 8, 3, -2, ... 
Step 1: Identify the first term ($a$), common difference ($d$), and number of terms ($n$).
First term, $a = 8$
Common difference, $d = 3 - 8 = -5$
Number of terms, $n = 22$ 
Step 2: Recall the formula for the sum of the first $n$ terms of an AP. $Sn = \frac{n}{2} 2a + (

Question 3

Check whether 301 is a term of the list of numbers 5, 11, 17, 23, ...

Accepted Answer

Given list of numbers: 5, 11, 17, 23, ... 
Step 1: Check if the sequence forms an AP. $11 - 5 = 6$ $17 - 11 = 6$ $23 - 17 = 6$
Since the difference between consecutive terms is constant ($d = 6$), the given list is an AP with first term $a = 5$ and common difference $d = 6$. 
Step 2: Assume that

Question 4

Find the sum of all odd integers between 0 and 50.

Accepted Answer

Step 1: Identify the sequence of odd integers between 0 and 50.
The odd integers between 0 and 50 are: 1, 3, 5, 7, ..., 49.
This forms an Arithmetic Progression where:
First term, $a = 1$
Common difference, $d = 3 - 1 = 2$
Last term, $an = 49$ 
Step 2: Find the total number of terms ($n$).
Us

Arithmetic Progressions