Question

The sum of 300 terms of the series 2 + 5 + 7 + 4 + 10 + 10 + 6 + 15 + 13 + 8 + 20 + 16 + ... is?

Answer 1

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Step-by-step explanation:

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Answer 2

Answer:

The sum of 300 terms of the series $2 + 5 + 7 + 4 + 10 + 10 + 6 + 15 + 13 + 8 + 20 + 16 + ...$ is $181800$

Step-by-step explanation:

• We find the common difference of the Arithmetic progression which is written as series. Then we write a few terms of both series to find two common terms which will form our new series of common terms. Using the two terms in the new series we find the common difference of the new series and find its sum using the formula for the sum of n terms.
• In an AP, first term is a, common difference is d and the number of term is n, then the nth term is given by $a_n=a+(n-1)d$
• The sum of n terms of an AP is given by $Sn=\frac{n}{2} (2a+(n-1)d)$

we can treat every two consecutive terms as one.

So, we will have a total of 300 terms of the nature:

(2 + 5) + (7 + 4) + (10 +10)+(6+15)+(13+8).... => 7, 11, 20,21,21....

We know the sum of n terms  $\frac{n(n+1)}{2}$

Now, a= 7, d=11-7=4 and n=300

Hence the sum of the given series is

$S= \frac{300}{2} *[2 * 7 + 299 * 4]$

$= > 150[1212]$

$= > 181800$