Question

hey guys i need the answers for the above 2 questions answer it fast plsss ...answer only if u knew it guys ​

Answer 1

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.