Question

Find the nth term of an A.P., whose sum of n terms is 4n^2-n

Answer 1

Step-by-step explanation:

▶AP is stands for arithmetic progression

▶Sn is stands for sum of all terms

▶nth term is denoted as tn

▶In an AP the difference between two consecutive terms is constant

▶here we know the condition,

tn = Sn - Sn-1

we have given,

Sn = 4n²-n _________(1)

we know,

tn = Sn - Sn-1_______(2)

from (1) and (2)

tn = (4n²-n)-(4(n-1)²-(n-1))

= (4n²-n )- (4(n² - 2n + 1) -n + 1 )

= (4n² - n) -(4n²-2n + 1 -n + 1 )

= 4n² - n - 4n² + 2n - 1 + n - 1

= 2n - 2

therefor, tn = 2n - 2