Question

in an A.P. the first term is 8, nth term is 33 and the Sun of the first n numbers is 164. Find n and d, the common difference​

Answer 1

Answer:

Given; a=8,an=33, sn=164

an=a+(n-1)d

33=8+(n-1)d

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

Sn=n/2(a+l)

164=n/2(8+33)

328=n(41)

n=8

Subs n in 1

(8-1)d=25

d=25/7

Hpe it hlps u

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

↠ 164 = n(41) /2

↠ 123 × 2 /41 = n

↠ n = 4 × 2

↠ n = 8

• Nth Term of the AP :

↠ l = a + [8 - 1]d

↠ 33 = 8 + 7d

↠ 33 - 8 = 7d

↠ 25 = 7d

↠ d = 3.4

∴ There will be 6 terms with 3.4 Common Difference in the Arithmetic Progresion.