Question

pls help me 13 and 14 questions

Answer 1

13) 2/3 , k , 5/8

To make an AP common difference must be equal

So,
k-2/3 = 5/8-k

=> 2k = 5/8+2/3

=> 2k = 31/24

=> k = 31/48

14)
a = 5 , d = 3
Tn = 50

a + (n-1)d = 50

5 + (n-1)3 = 50

3n-3 = 50-5

3n = 45+3

3n = 48 => n = 16

Answer 2

(13).

Given that 2/3,k,5/8 form an AP.

t1 = 2/3.

t2 = k

t3 = 5/8

Then the common difference = t2 - t1 = t3 - t2

                                                     k - (2/3) = (5/8) - (k)

                                                     2k = 2/3 + 5/8

                                                    2k = 2 * 8 + 5 * 3/24

                                                    2k = 16 + 15/24

                                                    2k = 31/24

                                                      k = 31/48.


(14) Given a = 5, d = 3, tn = 50 of an AP.

We know that tn = a + (n-1) * d

                        50 = 5 + (n - 1) * 3

                        50 = 5 + 3n - 3

                        50 = 3n + 2

                        n = 48/3

                        n = 16.


Hope this helps!