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Standard X

Mathematics

Formula for Sum of n Terms of an AP

If the sum of...

Question

Question 11
If the sum of the first n terms of an AP is $4 n - n^{2}$ , what is the first term $(t h a t i s S_{1})$ ? What is the sum of first two terms? What is the second term? Similarly find the $3^{r d}$ , the $10^{t h}$ and the $n^{t h}$ terms.

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Solution

$G i v e n t h a t, S_{n} = 4 n - n^{2} F i r s t t e r m, a = S_{1} = 4 (1) - (1)^{2} = 4 - 1 = 3 S u m o f f i r s t t w o t e r m s = S_{2} = 4 (2) - (2)^{2} = 8 - 4 = 4 S e c o n d t e r m, a_{2} = S_{2} - S_{1} = 4 - 3 = 1 C o m m o n d i f f e r e n c e (d) = a_{2} - a = 1 - 3 = - 2$
The $n^{t h}$ term of an A.P is given by
$a_{n} = a + (n - 1) d = 3 + (n - 1) (- 2) = 3 - 2 n + 2 = 5 - 2 n T h e r e f o r e, a_{3} = 5 - 2 (3) = 5 - 6 = - 1 a_{10} = 5 - 2 (10) = 5 - 20 = - 15 H e n c e, t h e s u m o f f i r s t t w o t e r m s i s 4. T h e s e c o n d t e r m i s 1. T h e 3^{r d}, 10^{t h}, a n d n^{t h} t e r m s a r e - 1, - 15, a n d 5 - 2 n r e s p e c t i v e l y .$

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If the sum of the first n terms of an AP is (4n− $n^{2}$ ), what is the first term (that is $S_{1}$ )? What is the sum of first two terms? What is the second term? Similarly, find the $3^{r d}$ , the $10^{t h}$ and the $n^{t h}$ terms.

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If

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then
i)

S_{1} = a = ?

ii)

S_{2} = ?

iii)

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iv)

a_{3} = ?

a_{10} = ?

vi)

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If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms

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Formula for Sum of n Terms of an AP

Standard X Mathematics

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Question 11 If the sum of the first n terms of an AP is 4n−n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the 10th and the nth terms.

Question 11
If the sum of the first n terms of an AP is $4 n - n^{2}$ , what is the first term $(t h a t i s S_{1})$ ? What is the sum of first two terms? What is the second term? Similarly find the $3^{r d}$ , the $10^{t h}$ and the $n^{t h}$ terms.