Math, asked by dipesh5715, 9 months ago

if a=2,n=5 Sn=90 in an AP find d​

Answers

Answered by Anonymous
13

 \huge\underline{\bf \orange{Solution :}}

 \large:\implies \boxed{ \red{ \tt S_n =  \dfrac{n}{2} \bigg [2a + (n - 1)d \bigg]}}

: \implies  \tt 90 =  \dfrac{5}{2} \bigg [2 \times 2 + (5 - 1)d \bigg]

:\implies  \tt 90 =  \dfrac{5}{2} \bigg [4 + 4d \bigg]

:\implies  \tt 90 =  5 \big[2 + 2d  \big]

:\implies  \tt 90 = 10 + 10d

:\implies  \tt10d = 90 - 10

:\implies  \tt10d = 80

:\implies  \tt d =  \dfrac{80}{10}

 \large:\implies\boxed{ \tt \blue{ d = 8}}

Answered by Skyllen
9

Given:-

  • First term = a = 2
  • No. of terms = n = 5
  • Sum of terms = Sn = 90

To find:-

  • Value of d (common difference).

Solution:-

 \sf \implies S_{n}  = \dfrac{n}{2} \bigg[ \: 2a + (n - 1)d \bigg]

\sf \implies 90 = \dfrac{5}{2} \bigg[ 2(2) + (5 - 1)d \bigg]

\sf \implies 90 = \dfrac{5}{2} \bigg[ 2(2)+(5-1)d \bigg]

\sf \implies 180 = 20+20d

\sf \implies 20d = 160

\sf \implies d = \dfrac{\cancel{160}}{\cancel{20}}

\sf \implies  \boxed{\boxed{ \purple{ \bf{d = 8}}}}

 \bf \therefore \underline{Value \: of \: d \: is \: 8}.

_____________________________________

In AP, there are three main terms, which are known as:

  • Common difference (d)
  • An (nth term of AP)
  • Sum of the first nth terms (Sn)

These three terms represents the characteristics of AP.

Common difference (d)

We can find the value of d, by subtracting 1st term from the 2nd term of AP.

Like, AP = 2,4,6,8

Common difference will be, 4 - 2 = 2

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