Question

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

Answer 1

1. Given a=8
2. nth term in AP is a+(n-1)d           (d is common difference)
3. Given nth term is 33  i.e, a+(n-1)d=33
4. 8+(n-1)d=33
5. (n-1)d=25------------>1
6. Also given sum of first n term is 123 i.e, (n/2)(2a+(n-1)d)=123
7. from   1    we get (n/2)(16+25)=123
8. from this we get n=6
9. On substitutine n in 1 we get 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.