Problem Solving (PS) | Re: The function is defined as follows: f(x+1) = 3x + 2. What is f(1)

f(x+1) = 3x + 2 and we need to find the value of f(1) + f(2) + f(3) +…+ f(9) +f(10)?

Let's solve the problem using twomethods

Method 1: Arithmetic ProgressionLogic

f(x+1) = 3x + 2
f(1) = 3*0 + 2 = 2
f(2) = 3*1 + 2 = 5
....
f(10) = 3*9 + 2 = 29

It is an Arithmetic series with number of terms = 10 and Sum of n terms of an Arithmetic Series is a multiple of\(\frac{n}{2}\) =\(\frac{10}{2}\) =5

Watch thisvideo to know about the Basics of ArithmeticSequence

Only, answer choice which is a multiple of 5 isC

Method 2: Arithmetic ProgressionSum

Watch thisvideo to know about the Basics of ArithmeticSequence

Sum =\(\frac{n}{2} * (2a +(n-1)*d)\) =\(\frac{10}{2} * (2*2 +(10-1)*3)\)
= 5 * (4 + 27) = 5 * 31 = 155

Solving using other formula for Sum =\(\frac{n}{2}\) * (First Term + Last Term) = 5 * (2 + 29) = 5 * 31 = 155

So, Answer will beC
Hope ithelps!

Watch the following video to learn the Basics of Functions and CustomCharacters

Iframe
...

Statistics : Posted by BrushMyQuant • on 01 Jun 2023, 06:30 • Replies 2 • Views 558

---