Question

a=8, an=62, sn=210. Find n and d.

Answer 1

First of all As We know that Sn = (n/2)[a + l] where l is the last term or nth term Hence 210 = (n/2)[8 + 62] 210 = (n/2)[70] 35n = 210 Therefore, n = 6 Recall an = a + (n - 1)d Tht is 62 = 8 + 5d 54 = 5d ∴ d = 54/5 So then n = 6 d = 54/5

Answer 2

We know,
a=8
a(n)=62
s(n)=210

We know,
a(n) = a + (n-1)d

Also
S(n) = n(a + a(n)) / 2
⇒210 = n (8 + 62) / 2
⇒420 = 70n
⇒n = 6

a(n) = a + (n-1)d
⇒62 = 8 + (6-1)d
⇒62 = 8 + 5d
⇒54 = 5d
⇒d = 10.8