Question

The second term from beginning and end of an A.P. are 9 and 39 respectively. If the sum of its terms is 192, then the number of terms will be. guys plz tell me this question fast​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The number of terms is 8.

Given:

Second term from beginning = 9

Second term from end = 39

Sum of terms = 192

To find: Number of terms

Solution:

Let the first term = a

Let common difference = d

Let the number of terms = n

We know that,

a₂ = a + (2 - 1)d = 9 (given)

⇒ a + d = 9

Also,

$a_{n-1}$ = a + (n - 2)d = 39 (given)

It is given that

Sum = n/2 [a + aₙ] = 192

⇒ n[a + (39 + d)] = 384

⇒ n[a + d + 39] = 384

⇒ n[39 + 9] = 384

⇒ 48n = 384

⇒ n = 8

∴ There are 8 terms in the AP.

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