Question

the sum of 7 term of an ap is 63 and the sum of its next 7 term is 120 find the nth term

Answer 1

let the first term be 'a'
Common difference be 'd'
n = 7
s7 = 63
sn = n/2 [ 2a + (n-1)(d) ]
Then
s7 = 7/2 [ 2a + (n-1)(d) ]
63 = 7/2 [ 2a + nd - d ]
126 = 14a + 7nd - 7d. {eq.1}



For the next 7 terms
a = a8
a = a + 7d

n = 7
s7 = 120
s7 = 7/2 [2(a+7d) + (n-1)(d)]
120 = 7/2 [ 2a + 14d + nd - d ]
240 = 14a + 91d + 7nd. {eq.2}