Question

If the nth term of an A.P is 63 and sum of nth term of an A.P is 123.Find n and d​

Answer 1

Answer:

an = a +( n-1 ) d

a63 = a + ( 63 -1 ) d

a63 = a + 62d

a + 62d = 63--------1

Step-by-step explanation:

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

s123 = 123/2 [ 2a + ( 123-1 ) d ]

2a + 122d = 123--------2

multiple 2 from equ 1

2a + 124d = 126 -------3

subtract equ 2 from equ 3

2a + 124d = 126

2a + 122d = 123

- - -

0 2d = 3

d = 3

2

put value of d in equ 1

a + 62d = 63

a + 62(3)= 63

2

a + 186 = 63

2

a + 93 = 63

a = 63 - 93

a = -30

an = a + ( n-1 ) d

63 = -30 + ( n-1 ) 3

2

63+30 = n-1 × 3

2

93 = n-1 × 3

2

93 × 2/3 = n-1

186/3 = n-1

62 = n-1

n = 62 +1

n = 63