Question

a=8, Tn=33, Sn=123, find d and n.

Answer 1

Hi ,

It is given that ,

In A.P , first term = a = 8 ,

Let common difference = d

nth term = Tn = 33

********************************************

If a , d are first term and common

difference of an A.P

nth term = Tn = a + ( n - 1 )d

Sum of n terms = Sn = n/2 [ a + Tn ]

***********************************************

1 ) Sn = 123

n/2 [ 8 + 33 ] = 123

( n/2 ) × 41 = 123

n = ( 123 × 2 )/41

n = 6

2 ) Tn = 33

a + ( n - 1 )d = 33

8 + ( 6 - 1 )d = 33

5d = 25

d = 25/5

d = 5

Therefore ,

d = 5 , n = 6

I hope this helps you.

: )

pls mark it as brainliest

Answer 2

Answer:

n = 6 , d = 5

Step-by-step explanation:

Tn = a + (n-1)d            -1

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

Sn = (n/2) {a + Tn}

123 = (n/2) (8 + 33)

123 * 2 = n * 41

n = 6

Put n=6 in eq.1

33 = 8 + (6-1)d

25/5 = d

d = 5

MARK MY ANSWER AS BRAINLIEST PLEASE