Series Identification: Arithmetic Progression
The given series is $8, 19, 30, \dots$. To understand the pattern, let's find the difference between consecutive terms:
- $19 - 8 = 11$
- $30 - 19 = 11$
Since the difference between consecutive terms is constant (11), this is an arithmetic progression (AP). In an AP, each term after the first is obtained by adding a fixed, non-zero number called the common difference.
Calculating the 10th Term
We need to find the 10th term of this series. We can use the formula for the $n$-th term of an arithmetic progression:
$$a_n = a_1 + (n-1)d$$
Where:
- $a_n$ is the $n$-th term (the term we want to find).
- $a_1$ is the first term of the series.
- $n$ is the term number.
- $d$ is the common difference.
Applying the Formula
From the given series $8, 19, 30, \dots$:
- The first term, $a_1 = 8$.
- The common difference, $d = 11$.
- We want to find the 10th term, so $n = 10$.
Step-by-Step Calculation
- Substitute the values into the formula:
$$a_{10} = 8 + (10-1) \times 11$$
- Calculate the value inside the parenthesis:
$$a_{10} = 8 + (9) \times 11$$
- Perform the multiplication:
$$a_{10} = 8 + 99$$
- Perform the addition:
$$a_{10} = 107$$
Therefore, the 10th term of the arithmetic series $8, 19, 30, \dots$ is 107.
Important Questions from Arithmetic Progression
If the arithmetic mean of a, b, c is \(\rm \frac M 3\) and \(\rm \frac{1}{a} + \frac{1}{b} = -\frac{1}{c} \) , then the arithmetic mean of a 2, b 2, c 2 is
A person saves Rs. 1000 more than he did the previous year. If he saves Rs. 2000 in the first year, in how many years will he save Rs. 170000?
How many natural numbers lie between 3 and 200 which are divisible by 7?
The arithmetic mean of 16 student's scores is 320. Find the sum of these scores.
How many three-digit numbers are divisible by 5?
