Question

Given the arithmetic series,4+9+14+,,,,,,+54 find the sum of the series

Answer 1

▪Given :-

An Arthematic Series :

$\large\mathfrak{4+9+14+ \: .\: . \:. \: +54}$

▪To Find :-

Sum of Given Series

▪Formulas

1》 for Sum :-

$\bf S_n= \dfrac{ n}{2} \bigg \{a + a_n\bigg \}$

2》For nth term

$\bf a_n = a + (n - 1)d$

Where ,

a = First term

$\sf{a_n}$ = nth Term

n = Number of terms

d = Common difference

▪Solution :-

Here

a = 4

d = 5

$\sf{a_n}$ = 54

《Calculating Number of Terms》

Using Formula of nth term :-

$54 = 4 \: + \: (n - 1)5 \\ \\ 5n - 5 = 54 - 4 \\ \\ 5n = 50 \\ \\ n = \frac{ \cancel{50 {}} }{ \cancel{5}} \\ \\ \Large \purple{ \implies  \underline {\boxed{{\bf n = 10} }}}$

《Calculating Sum》

Using Formula For Sum :-

$\sf SUM = \dfrac{10}{2} \bigg \{ 4 + 54\bigg \} \\ \\ = 5(58) \\ \\\Large \purple{ \implies  \underline {\boxed{{\bf SUM = 290} }}}$

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