The sums of n terms of two arithmetic progressions are in the ratio 5 n+4: 9 n+6.

Name: Problem 9, Chapter 9: NCERT Class 11 - Math
Uploaded: 2021-06-14T04:36:30-08:00
Duration: 5 min 23 s
Channel: Suman Saurav Thakur
Description: The sums of n terms of two arithmetic progressions are in the ratio 5 n+4: 9 n+6.

step 1 Hello, we have problem number nine. In this problem, we have the sum of n terms of two arithmeti

The sums of n terms of two arithmetic progressions are in...

Key Concepts

Arithmetic Progression

An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the common difference. The concept of an AP is fundamental in sequence and series problems because it provides a structured way to represent linear relationships among the terms.

Sum of an Arithmetic Progression

The sum of an arithmetic progression is found using a formula that takes into account the first term, the common difference, and the number of terms. Typically, the formula S? = n/2 [2a + (n ? 1)d] or S? = n*(first term + last term)/2 is used. This formula is essential when comparing or equating sums of different progressions, as it expresses the sum in terms of easily manipulable variables.

Ratio Analysis of Algebraic Expressions

When sums or other quantities from different sequences are given in a ratio, it implies a proportional relationship between the corresponding algebraic expressions. Analyzing such ratios involves comparing the coefficients of like terms, typically after expressing both sums in a common variable format. This method allows for the extraction of relationships between the underlying parameters of the sequences.

Equating Coefficients

Equating coefficients is a strategy used in problems where two polynomial expressions are set equal to one another, often in the context of ratios or identities. By matching the coefficients of corresponding powers of the variable in each expression, one can derive equations that must hold true. This method is particularly useful in identifying the relationships between parameters, such as the first term and common difference in arithmetic progressions.

Please give Ace some feedback