Question

Sum of n terms of an AP is 54.its first term is 21 and common difference is-3.justify the answer for two value of n.

Answer 1

Answer:

sum= n/2 [2a + (n-1) d]= 54

a (first term)= 21

d (common difference)= 3

therefore, putting the values of 'a' and 'd' in the equation we get,

54= n/2 [2*21 + (n-1) 3]

⇒54= n/2 [42 + 3n - 3]

⇒108 = n [39+ 3n]

⇒108 = 39n +3n²

dividing the equation with 3, we get,

⇒36= 13n + n²

⇒n² + 13n - 36 = 0

⇒n=( -13±√13²-4*-36)/ 2

⇒n= (-13 ±√256+144)/2

⇒n= (-13±√400)/2

⇒n= (-13+20)/2 or (-13-20)/2

⇒n= 7/2 or -33/2

⇒n= 3.5 or -16.5

thus n has two values since it obtains a square form. a square number always has two roots. (not necessarily real roots)

Step-by-step explanation:

Answer 2

Answer:

take this..................