Find Number of Terms When Sum of N Terms, First Term and Common Difference are Given


 
 
Concept Explanation
 

Find Number of Terms When Sum of N Terms, First Term and Common Difference are Given

Find Number of Terms When Sum of N Terms, First Term and Common Difference are Given : We will use the formula

 S_n=large frac{n}{2}left [ 2a+(n-1)d right ]

Example: How many odd integers beginning with 15 must be taken for their sum to be equal to 975?

Solution:     The odd integers beginning with 15 are follows 15, 17,19,...

This forms an A.P. with

first term , a =15 and

common difference, d =17-15 =2

Let 'n' terms of the A.P. be taken to make the sum 975

large Rightarrow 15+17+19+.....n; terms = 975

large Rightarrow s_{n}=frac{n}{2}left [ 2a+(n-1) dright ]=975

Substituting thevalue of 'a' and 'd ' in large s_{n}

large Rightarrow frac{n}{2}left [ 2times 15+(n-1) 2right ]=975

large Rightarrow 15n +(n-1)n=975

large Rightarrow 15n +n^{2}-n=975

large Rightarrow n^{2}+14n-975=0

large Rightarrow n^{2}+39n-25n-975=0

large Rightarrow n(n+39)-25(n+39)=0

large Rightarrow (n-25)(n+39)=0

large Rightarrow n=25 ;or;n=-39

But n= -39 is rejected since number of terms cannot be negative

large therefore Number of odd integers beginning with 15 to make the sum equal to 975=25

Sample Questions
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Question : 1

How many terms of an AP series 3,6, 9, 12, 15 will sum up to 108

Right Option : C
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Explanation
Question : 2

The sum of first n terms of an AP is 126 if the first term and the common difference are 11 and 4 respectively . Which of the following values holds true for n?

Right Option : D
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Explanation
Question : 3

The sum of the first n terms of an AP is 114. If the first term and the common difference of the AP are 12 and 11 respectively,  which of the following values holds true for n ? 

Right Option : C
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Explanation
 
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