Question

in an ap the first term is 8, nth term is 33 and sum to first n terms is 123. Find n and d, the cimmon difference

Answer 1

Given :- a ( first term ) = 8

an = 33


Sn = 123

an = a + ( n - 1 )d

33 = 8 + ( n - 1 )d

25 = ( n - 1 )d ...... ( i )

Sn = 123

$\frac{n}{2} (2a + (n - 1)d) = 123$


n ( 16 + 25 ) = 246

41n = 246

n = 6


Putting value of n in ( i )

25 = ( n - 1 )d

25 = 5d

5 = d


n = 6
d ( common difference ) = 5

Answer 2

Answer:

• First Term ( a ) = 8
• Last Term ( l ) = 33
• Sum of n terms ( Sn ) = 123

• Sum of Nth Terms of AP :

↠ Sn = n(a+l) /2

↠ 123 = n(41) /2

↠ 123 × 2 /41 = n

↠ n = 3 × 2

↠ n = 6

• Nth Term of the AP :

↠ l = a + [n - 1]d

↠ 33 = 8 + 5d

↠ 33 - 8 = 5d

↠ 25 = 5d

↠ d = 5

∴ There will be 6 terms with 5 Common Difference in the Arithmetic Progresion.