Question

How many terms of the A.P. 3, 9,15,……..must be taken to give the sum 192.​

Answer 1

Answer:

The required number of terms of the given A.P is 8.

Step-by-step explanation:

In an A.P., the sum of first n terms is given by,

$\boxed{S_n=\dfrac{n}{2}[2a+(n-1)d]}$

where

a denotes the first term

d denotes the common difference

The given A.P. is 3, 9, 15, ...

first term, a = 3

common difference is the difference between a term and it's preceding term.

d = 9 – 3 = 6

Let the number of terms of thr given A.P be n such that their sum is 192.

192 = n/2[2(3) + (n – 1)(6)]

192 × 2 = n(6 + 6n – 6)

384 = n(6n)

384 = 6n²

n² = 384/6

n² = 64

n = ±8

number of terms can't be negative

hence, n = 8

Therefore, the required number of terms is 8

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Know more :

Arithmetic Progression is the sequence of numbers such that the difference between any two successive numbers is constant.

General form of A.P is : a, a+d, a+2d,...

The nth term of an A.P is given by,

$\underline{\tt a_n=a+(n-1)d}$