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Standard X

Mathematics

Common Difference

Let there be ...

Question

Let there be an A.P with first term $a$ , common difference $d$ . If $a_{n}$ denotes its $n$ th term and $S_{n}$ the sum of first $n$ terms, find
$n$ and $S_{n}$ , if $a = 5, d = 3$ and $a_{n} = 50$

n = 15

;

S_{n} = 430

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n = 16

;

S_{n} = 440

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n = 15

;

S_{n} = 450

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n = 16

;

S_{n} = 460

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Solution

The correct option is B $n = 16$ ; $S_{n} = 440$
Formula and Given,

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

$50 = 5 + (n - 1) 3$

solving the above equation, we get,

$n = 16$

$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

$= \frac{16}{2} [2 (5) + (16 - 1) (3)]$

solving the above equation, we get,

$∴ S_{n} = 440$

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Let there be an A.P with first term a, common difference d. If an denotes its nth term and Sn the sum of first n terms, findn and Sn, if a=5,d=3 and an=50

The correct option is B n=16; Sn=440Formula and Given,an=a+(n−1)d50=5+(n−1)3solving the above equation, we get,n=16Sn=n2[2a+(n−1)d]=162[2(5)+(16−1)(3)]solving the above equation, we get,∴Sn=440

Let there be an A.P with first term $a$ , common difference $d$ . If $a_{n}$ denotes its $n$ th term and $S_{n}$ the sum of first $n$ terms, find
$n$ and $S_{n}$ , if $a = 5, d = 3$ and $a_{n} = 50$

The correct option is B $n = 16$ ; $S_{n} = 440$
Formula and Given,

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

$50 = 5 + (n - 1) 3$

solving the above equation, we get,

$n = 16$

$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

$= \frac{16}{2} [2 (5) + (16 - 1) (3)]$

solving the above equation, we get,

$∴ S_{n} = 440$