find the sum of first 20terms of the arithmetic progression 3,8,13…. using the formula​

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1. Given:-

   • An A.P = 3, 8, 13, . . . .

   To Find:-

   • Sum of first 20 terms of an A.P.

   Formula Used:-

   • [tex]{\boxed{\bf{S_n = \dfrac{n}{2}[2a+(n-1)d]}}}[/tex]

   Here,

   • [tex]\bf S_n [/tex] = Sum of n terms

   • a = First term of the A.P

   • d = Common Difference

   • n = No. of terms in an A.P

   Solution:-

   Using Formula,

   [tex]\bf :\implies\:S_n = \dfrac{n}{2}[2a+(n-1)d][/tex]

   Here,

   • a = 3

   • d = 8 – 3 = 5

   • n = 20

   Putting values,

   [tex]\sf :\implies\:S_{20} = \dfrac{20}{2}[2\times3+(20-1)5][/tex]

   [tex]\sf :\implies\:S_{20} = 10[6+19\times5][/tex]

   [tex]\sf :\implies\:S_{20} = 10[6+95][/tex]

   [tex]\sf :\implies\:S_{20} = 10\times101[/tex]

   [tex]\bf :\implies\:S_{20} = 1,010[/tex]

   Hence, The Sum of first 20 terms on given A.P is 1,010.

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