Math, asked by baddarabdulrazzaq, 7 hours ago

Find the sum of the AP 4,8,12,16, upto 40

Answers

Answered by xSoyaibImtiazAhmedx
1

Given

A.P. — 4 , 8 ,12 ,16,...40

Here ,

  • a ( first term ) 4
  • d ( common difference ) 4
  • l ( last term ) 40

Let, number of terms be n .

Now,

 \bold{★ \:  \:  \:  \: l \:  = a \:  + (n - 1)d}

 \implies \: 40 = 4 + (n - 1)4

\implies \: 40 - 4 =(n - 1)4

\implies \: 36 =(n - 1)4

\implies \: n - 1 =  \frac{36}{4}

\implies \: n - 1 =  9

\implies \: n  =  9 + 1

\implies \:  \underline \bold{n  =  10}

Sum of the A.P.

 \bold{S_n = \frac{n}{2}(a + l)}

 \implies \bold{ S_{10 }=  \frac{10}{2} (4 + 40)}

 \implies \bold{ S_{10 }=  \frac{10}{2}  \times 44}

\implies \bold{ S_{10 }=  {10}  \times 22}

\implies  \boxed{\bold{ S_{10 }=  220}}

\Large{\colorbox{yellow}{\underline{\underline{♠Answer♠:—\:\:220} }}}

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