Question

7. The sum of the 10th and the 20th terms of an
A.P. is 98 and their product is 2176. Find the
first term and the common difference.
(4 marks)​

Answer 1

Answer:

The common difference is equal to the value of the last term minus that of the term second to last.

This can be written as D = A(N) - A(N-1)

Where A is the Nth term and N is the number of terms preceding to and including this one.

Nth term = First term + (number of terms - 1) * common difference.

First term = -5

Number of terms = 20

-5 + 19* common difference = 90

Add 5 to both sides

19* common difference = 95

95/ 19 = 5

So the common difference is 5.

And the Nth term = -5 + 5n -5 which is 5n -10

We can plug this into the common difference equation (5n - 10 (20)) - ((5n - 10 (19)) = 90 - 85 = 5

So the common difference is indeed 5.

This is algebraic proof which is required for harder examples but in this case, you could simply subtract 1 from the position of the last term (20) to give 19 and divide the difference between the values (95) by 19 on a linear graph to give the value of 5.

Step-by-step explanation:

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