Math, asked by jaindrasingh5171, 11 months ago

Find the sum of the first 25 terms of an ap whose n term is given by tn = 7-3n

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Answered by rishu6845
4

Answer:

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Answered by Anonymous
5

 \orange{ \rm \boxed{ \star \: given - }}

 \boxed{ \rm \:a   _{n} = (7n - 3n)}

 \boxed{ \large \rm \to \: to \: find \: out  \implies  \: s_{25} =  {?}}

 \pink{ \boxed{ \rm \:solution:-}}

 \rm \: t _{n}  = (7n - 3n) \implies \: t _{1} = (7 - 3  \times 1) \: and \: t _{2} = (7 - 3 \times 2) = 1 \\  \rm \therefore \: a = 4 \: and \: d = (t _{2} - t  _{1}) = (1 - 4) =  - 3

 \rm \:  \therefore \: sum \: of \: 25 \: terms \: is \: given \: by \\ \rm s _{25} =  \frac{n}{2}  \times   \large( \small \: 2a + (n - 1)d \large) \:  \: where \: n = 25

 =  \large{ \frac{25}{2} }  \times ( \small2   \times 4 + (25 - 1) \times ( - 3)  \large) \:   =  \frac{25}{2 }  \times ( - 64)

 = 25 \times ( - 32) =  - 800

 \large \red{ \boxed{ \rm \: hence \: the \: sum \: of \: first \: 25 \: term \: is - 800}}

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