Question

In an ap 1st term is 8 nth term is 33 and sum if first n terms is 123. Find n and commin difference

Answer 1

Given, a=8 ,an=l=33 ,Sn=123

Sn = n/2×(a+l)
123 = n/2×(8+33)
123 = n/2×41
123/41 = n/2
3×2 = n
n = 6
therefore, an = a+(n-1)d
33 = 8+(6-1)d
33-8 = 5d
25 = 5d
d = 5

Therefore, n = 6 , d = 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.