Question

How many terms of the series 51,47, 43,39..... Be taken so that sum is 330

Answer 1

Explanation:

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Answer 2

Answer:

Required number of terms are 10.

Explanation:

Here given series is 51,47, 43,39....

Common difference of this series is (-4)

So this is an Arithmetic progression.

We want to find number of terms of this series.

It is given that sum of the series is 330.

We know,

Sum of n th series in AP series $= \frac{n}{2} (2a + (n - 1)d)$

Where n is the number of terms,a is the first term of the series and d is the common term.

Here,

$a = 51$ and $d = - 4$

According to question,

$\frac{n}{2} (2 \times 51 + (n - 1) \times ( - 4)) = 330 \\ \frac{n}{2} (102 - 4n + 4) = 330 \\ n(51 - 2n + 2) = 330 \\ 51n - 2 {n}^{2} + 2n = 330 \\ 2 {n}^{2} + 53n - 330 = 0 \\ (n - 10)(2n - 33) = 0$

If product of two term is zero then they are separately zero.

So,

$(n - 10) = 0 \\ n = 10$

and

$(2n - 33) = 0 \\ 2n = 33 \\ n = \frac{33}{2}$

Number of term (33/2) is not possible.

So required value of n is 10.

Know more about Arithmetic progression:

1) https://brainly.in/question/4219484

2) https://brainly.in/question/2768711