Find The Value of First Term when Nth Term, Number of Terms and Common Difference are Given


 
 
Concept Explanation
 

Find The Value of First Term when Nth Term, Number of Terms and Common Difference are Given

Find The Value of First Term When Nth Term, N and the Commom Difference Is Given.: We will use the formula for the general term. Putting the value of n , d and Nth Term we will find a.

Example:  Find the Value of the first term when common diffrenece is 10 and  the 11th term of the AP is 275.

Solution :    Here, d= 10, n= 11 and large a_11=275

We have                large a_{n}=a+(n-1)d

So,                         large a_{16}=3+(16-1)times d

                                  275 = a+10 X 10

                                 275 = a +100

                                    a = 175

Therefore , the First Term  a= 175.

Example: A manufacturer install a machine at certain amount. At the end of 9 years the machine has a value of Rs 5000. If the annual depreciation has been constant for Rs 300. Find amount of machine at the begining.

Solution: a= ?

                d= -300   [As the annual depreciation has been constant for Rs 300]

                n= 9

               a_n=5000

large a_{n}=a+(n-1)d

5000 = a + (9-1) (-300)

5000 = a -2400

a= 7400 Rs.

The amount of machine at the begining = 7400 Rs.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

For an AP, the large {5^t^h} term is 65 and common difference is 11 The first  term of the AP is _______________

Right Option : C
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Explanation
Question : 2

For an AP, the large {21^t^h} term is 20 and the common difference is - 5. The first term of the AP is

Right Option : A
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Explanation
Question : 3

For an AP the large 18^{th} term is 62 and the common difference is 3,  the first term of the AP is ____________

Right Option : A
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Explanation
 
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