Question 1
The sum of the first ten terms of an Arithmetic
Progression (A. P.) is 130. If the fifth term is 3
times the first term, find the:
a. common difference;
b. first term;
c. number of terms of the A. P. if the last term is
28.

  a. 2

  b. 4

  c. 13

Step-by-step explanation:

The general term of an arithmetic progression is ...

  an = a1+d(n-1)

where a1 is the first term, and d is the common difference.

The sum of n terms is ...

  Sn = n(2a1 +d(n -1))/2

__

The given relations tell us ...

  S10 = 10(2a1 +9d)/2 = 10a1 +45d = 130

and

  a5 = 3a1

  a1 +4d = 3a1

  4d = 2a1

  2d = a1

Using this in the equation for S10 above, we have ...

  10(2d) +45d = 130

  d = 130/65 = 2

___

(a) The common difference is 2.

  d = 2

__

(b) The first term is a1 = 2d = 2(2)

  a1 = 4.

__

(c) an = 28 = 4 +2(n -1)

  24 = 2(n -1)

  12 = n -1

  13 = n

The 13th term is 28.

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

they are simplified

step-by-step explanation: