Question

in an AP the first term is 1 and thecommon difference in 4.How many terms of the ap must be taken to 120​

Answer 1

Answer:

8

Step-by-step explanation:

The sum of n numbers of A.P is

Sn=n/2(2a + (n-1) d)

Where, a is the first term a=1,

d is the common difference d=4 and

Sn= 120 the sum

Substitute the values,

120= n/2( 2(1) + (n-1) (4) )

120×2=n (2 + 4n -4 )

240= n(4n -2 )

240= 4n^2 - 2n

240= 2( 2n^2 - n )

240/2 = 2n^2 - n

120= 2n^2 - n

0= 2n^2 - n - 120

0= ( n-8 ) ( 2n + 15 )

n=8 or n= -15/2

n can never in fraction and negative

So, reject n= -15/2

So, n=8.

So, 8 terms of ap must be taken to 120