Sequence Tenth Term Calculation
The problem asks for the 10th term of the sequence 2, 5, 8, 11, ....
Identifying Sequence Properties
This sequence is an Arithmetic Progression (AP) because the difference between consecutive terms is constant.
- First term ($a$): 2
- Common difference ($d$): $5 - 2 = 3$.
Arithmetic Progression Formula
The formula to find the $n$-th term ($a_n$) of an AP is:
$ a_n = a + (n-1)d $Where:
- $a_n$ is the n-th term
- $a$ is the first term
- $n$ is the term number
- $d$ is the common difference
Calculating the Tenth Term
We need to find the 10th term, so $n=10$. Plugging the values into the formula:
$ a_{10} = 2 + (10-1) \times 3 $
$ a_{10} = 2 + (9) \times 3 $
$ a_{10} = 2 + 27 $
$ a_{10} = 29 $
Final Answer
The tenth term of the sequence is 29.
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 $10^{\text{th}}$ term of the Arithmetic Progression $2, 7, 12, \dots$ is:
- 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:
- 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?
