hey guys i need the answers for the above 2 questions answer it fast plsss ...answer only if u knew it guys
Answers
1. an=37
a = 213
d = -8
a + (n + 1) d =37
213 + (n + 1)(-8) = 37
213 -8n -8 = 37
213 - 8 - 37 = 8n
168 = 8n
∴ n = 168 ÷ 8
⇒ n = 21
Here, as n is odd, we use the formula:
[n+1] 21 + 1
------- = ---------
2 2
= 11th term
Hence,
a11 = a + (11 - 1)d
= 213 + 10 × -8
= 213 - 80
= 133
∴ The middle term of the AP is 133.
2. Given,
5 years ago, A was thrice as old as B
∴ (A - 5) = 3(B - 5)
A - 5 = 3B - 15
⇒ A = 3B - 10 → 1
Ten years later, A shall be twice as old as B
∴ (A + 10) = 2(B + 10)
A + 10 = 2B + 20
⇒ A - 2B = 10 → 2
Substituiting A in the 2nd eqn.,
3B - 10 - 2B = 10
B - 10 = 10
∴ B = 20
A = 3B - 10
= 3(20) - 10
= 60 - 10
∴A = 50
Hence, the current ages of A is 50 and B is 20.