Question

In an

a.P., the first term is 8, nth term is 33 and sum of first n terms is 123. Find n and d, the common difference.

Answer 1

Answer:

n = 6, d = 5 ,

Step-by-step explanation:

nth term of an A.P = a+(n-1)d

Given, nth term = 33 = 8+(n-1)d

25 = (n-1)d =>> (n-1) = 25/d

1st term = a = 8

Sn = n/2[2a+(n-1)d] = 123

= n/2[2(8)+(n-1)d] = 123

= n/2[16+25/d×d] = 123

= n/2(16+25) = 123

= n/2(41) = 123

= n/2 = 3

= n = 6

Sum of 1st 6 terms = 123

(n-1) = 25/d

6-1 = 25/d

d = 25/5 = 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.