Arithmetic Sequence Worksheet Solution5





In the page arithmetic sequence worksheet solution5 you are going to see solution of each questions from the arithmetic sequence worksheet.

(15) If m times the mth term of an A.P is equal to the n times the nth term, then show that the (m + n)th term of the A.P is zero

Solution:

m tm = n tn

m [ a+ (m - 1) d ] = n [ a+ (n - 1) d ]

m a + m d (m – 1)  = n a + n d (n – 1)

m a + m² d – m d  = n a + n² d – n d

m a - n a + m² d - n² d – m d  + n d = 0

a (m – n) + (m² - n² – m + n ) d = 0

a (m – n) + [ (m + n) (m - n) –( m - n ) ] d = 0

a (m – n) + (m – n) [ (m + n) – 1 ] d = 0

Divide by (m - n) => a + [ (m + n) – 1 ] d = 0

                                     t (m + n) = 0

Therefore the (m+n) th term of the A.P is zero.


(16) A person has deposited $25000 in an investment which yields 14% simple interest annually. Do these amounts (principal + interest) form an A.P? If so, determine the amount of investment after 20 years.

Solution:

Simple interest = PNR/100

                         = (25000 x 1 x 14)/100

                         = 3500

Amount = principal + interest

             = 25000 + 3500

            = 28500

Amount at the end of the first year = 28500

Amount at the end of second year = 28500 + 3500

                                                       = 32000

Amount at the end of third year = 32000 + 3500

                                                  = 35500

 

28500,32000,35500.,………………….

This is the arithmetic sequence. To find the amount of investment after 20 years we need to find 20th term

tn = a +(n - 1) d

a = 28500    d = 32000 – 28500

                       = 3500

t20 = 28500 + (20 - 1) 3500

      = 28500 + 19 (3500)

      = 28500 + 66500

      = 95000

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