Question

plese a swer both of them ples ​

Answer 1

Answer:

672 is the sum of the first 24 terms.

Step-by-step explanation:

an=a + (n-1)d      [where a=1st term of ap ,d=common difference,n=no. of terms]

given ,

an = 3+2n = a +dn -d

   here we can say that

3 = a - d

2n = dn

d=2

3 = a -2

a = 5

hence ,

the ap is :  5 ,7,9,11,13,15,17,.....

now sum of terms upto nth term

sn = n/2 (2a + (n-1)d )

s24 = 12 (2*5 + 23*2)

s24 = 12* (10 + 46)

s24 = 12 * 56

s24 = 672

Answer 2

$\huge\underline{ \mathrm{ \red{QueStiOn}}}$

Find the sum of first 24 terms of the list of Numbers. whose nth term is given by an=3+2n

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$\large\underline{ \underline{ \green{ \bold{Answer}}}}$

1. sum of 1st 24 terms = 672

$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanATiOn }}}}}}$

$\large\underline{ \underline{ \red{ \bold {Given}}}}$

an = 3+2n

$\large\underline{ \underline{ \red{ \bold {To \:Find}}}}$

we need to find the sum of 1st 24 terms.

⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \orange{ \bold{sOluTiOn}}}}$

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$\bf:\implies\:1st\:term = a_1= 3+2(1)$

$\bf:\implies\:a = 3 + 2 \\ \\ \bf:\implies\:a = 5$

$\bf:\implies\: second\:term=a_2=3+2(2)$

$\bf:\implies\:a_2=3+4$

$\bf:\implies\:a_2=7$

$\bf:\implies\:third \:term \:a_3=3+2(3)$

$\bf:\implies\:a_3=3+6$

$\bf:\implies\:a_3=9$

$\bf:\implies\:so\:the \: series=5,7,9.......$

$\bf:\implies\: common\: difference (d)=7-5=2$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\bf:\implies\:9-7=2$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\bf:\implies\:11-9=2$

$\bf\:so \: common\: difference=2\:$

${ \boxed{ \fbox { \pink {\bf{\:s_{n} = \frac{n}{2} (2a + (n - 1)d)}}}} }$

where n=24,

a = 5

d = 2

putting these values in the formula

$\bf:\implies=\frac{24}{2} [2\times5 + (24 - 1)2]$

$\bf:\implies=\frac{24}{2} [2\times5 + (23)(2)]$

$\bf:\implies=12[10+ 46]$

$\bf:\implies=12\times56$

$\bf:\implies=672$

hence sum of 1st 24 terms is 672.

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$\large\underline{ \mathrm{ \red{QueStiOn2}}}$

Find the distance between the points A (0,6) and B(0,-2)

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$\large\underline{ \underline{ \green{ \bold{Answer}}}}$

Distance between the points is 8units

$\large{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanATiOn }}}}}}$

$\large\underline{ \underline{ \red{ \bold {Given}}}}$

two points are given as A(0,6) and B(0,-2)

$\large\underline{ \underline{ \red{ \bold {To \:Find}}}}$

we need to find the distance between the two points.

⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \orange{ \bold{sOluTiOn}}}}$

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Using distance formula

$\: \: \: \: \: \: \: \: \: \: \: { \boxed{ \pink{\bf\:{\sqrt{(x_{2} -x_{1}) {}^{2} +(y_{2} - y_{1}) {}^{2} }}}}}$

$\bf\:x_1=0\\\bf\:x_2=0\\\bf\:y_1=6\\\bf\:y_2=-2$

$\bf: \implies \sqrt{(0 + 0) {}^{2} + ( - 2 - 6) {}^{2} } \\ \\ \bf : \implies \sqrt{0 + 64} \\ \\ \bf : \implies \sqrt{64} \\ \\ \bf : \implies=8 units$

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