Question

The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?

Answer 1

Concept:

An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between the terms remains constant.

Given:

An AP is given to us,

First-term is 6 and the sum of all the terms is 1800

To find:

The number of series

Solution:

An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between the terms remains constant.

We know that in this question an AP is given to us

Let's assume that there are n number of terms in the AP,

So, the sum of n terms is 1800

First-term = 6

Common difference = 6 (2nd term- first term)

The formula of AP is $\frac{n}{2} [2a+(n-1)d]$

So, by the formula of AP, we get

$1800 = \frac{n}{2} [12+(n-1)6]\\3600 = n[12+6n-6]\\3600 = 6n+6n^{2} \\6n^{2} +6n-3600 = 0\\n^{2} +n-600 = 0\\n^{2} +25n-24n-600 = 0\\n(n+25)-24(n+25)=0\\(n+25)(n-24)=0$

Now, we get two values of n, -25 and 24

Since the value of n can not be negative, we take 24 as our answer.

So, there are 24 terms in the AP whose sum is 1800.

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