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How many terms of the series 12, 16, 20, ..... must be taken t

Question

How many terms of the series $12, 16, 20, .....$ must be taken to make the sum equal to $208$ ?

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How many terms of the series

12, 16, 20, .....

must be taken to make the sum equal to

208

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

The given series is

12, 16, 20, .....

Let the number of terms in the series be

n

, such that the sum of

n

terms in the series is

208

The first term in the series be

a = 12

and the common difference be

d = 16 - 12 = 4

The sum of

n

terms in the series is

\frac{n}{2} (2 a + (n - 1) d)

, given that it is equal to

208

\Rightarrow \frac{n}{2} (2 a + (n - 1) d) = 208

\Rightarrow \frac{n}{2} (24 + (n - 1) \times 4) = 208

\Rightarrow n (n + 5) = 104 = 8 \times 13

\Rightarrow n = 8

Therefore we must take

8

terms in the series in order to make their sum equal to

208

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Question Text	How many terms of the series $12, 16, 20, .....$ must be taken to make the sum equal to $208$ ?
Answer Type	Text solution:1
Upvotes	150