Arithmetic Progression: Calculating the 10th Term
The problem asks for the 10th term of a given Arithmetic Progression (AP).
Understanding the Arithmetic Progression
- The sequence provided is 2, 7, 12, ...
- The first term ($a$) is 2.
- The common difference ($d$) is found by subtracting any term from its subsequent term: $7 - 2 = 5$ or $12 - 7 = 5$. Thus, $d = 5$.
- We need to find the 10th term, so $n = 10$.
Step-by-Step Solution
The formula for the $n^{\text{th}}$ term of an Arithmetic Progression is:
$a_n = a + (n-1)d$
Substitute the known values into the formula:
- $a = 2$
- $d = 5$
- $n = 10$
Calculate the 10th term ($a_{10}$):
$a_{10} = 2 + (10-1) \times 5$
$a_{10} = 2 + (9) \times 5$
$a_{10} = 2 + 45$
$a_{10} = 47$
The 10th term of the Arithmetic Progression is 47.
Similar Questions
- If the ratio of the 11th term of an AP to its 18th term is 2 : 3, find the ratio of the sum of its first five terms to the sum of its first 10 terms.
- If the sum of five consecutive multiples of 2 is 660, then find the largest number.
- The sum of the first 12 multiples of 6 is:
- What is the $50^{\text{th}}$ term of Arithmetic Progression 3, 8, 13, 18, 23, ........?
- The sum of all odd numbers between 0 and 52 is:
- The tenth term of the sequence 2, 5, 8, 11, ......will be:
- What is the sum of the first 12 multiples of 4?
- What is the sum of the squares of all two-digit numbers each of which is completely divisible by 4?
- What is the sum of the first 25 odd numbers?
- What is the value of k in the following Arithmetic progression?
$$15+13+11+9+ \dots +k = -105$$
Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
