Question

first term of an arithmetic progression is 8 and term is 33 and sum of first n term is 123 then find n and common difference d

Answer 1

a=8
L=33
Sn=n/2(a+l)
=123=n/2(8+33)
=123=n/2*41
=123=41n/2
=41n=246
=n=246/41
=n=6
Again,
L=33
a+(n-1)d=33
8+(6-1)d=33
8+5d=33
5d=33-8
5d=25
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.