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Standard VIII

Mathematics

Formula for sum of n terms of an AP

If the sum of...

Question

If the sum of the first $n$ terms of an $A . P$ is $4 n - n^{2}$ , what is the first term (i.e. $S_{1}$ )? What is the sum of first two terms? What is the second term? Also, find the $3 r d$ term, the $10$ th and the $n$ th terms ?

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Solution

Given
$S_{n} = 4 n - n^{2}$
Taking $n = 1$
$S_{1} = 4 \times 1 - 1^{2}$
$= 4 - 1$
$= 3$
So, Sum of first term of $A P$ is $3$
But sum of first term will be the first term
So, First term $= a = 3$

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If the sum of the first n terms of an A.P is 4n−n2, what is the first term (i.e. S1)? What is the sum of first two terms? What is the second term? Also, find the 3rd term, the 10th and the nth terms ?

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If the sum of the first $n$ terms of an $A . P$ is $4 n - n^{2}$ , what is the first term (i.e. $S_{1}$ )? What is the sum of first two terms? What is the second term? Also, find the $3 r d$ term, the $10$ th and the $n$ th terms ?

Given
$S_{n} = 4 n - n^{2}$
Taking $n = 1$
$S_{1} = 4 \times 1 - 1^{2}$
$= 4 - 1$
$= 3$
So, Sum of first term of $A P$ is $3$
But sum of first term will be the first term
So, First term $= a = 3$