Math, asked by lakshit00135, 9 months ago

the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 - 3n

Answers

Answered by ahmedabaszaidi9
4

aₙ=a+(n-1)d

aₙ=7-3n

  a₁=7-3=4

a₂=7-3(2)

   =1

d=a₂-a₁=1-4=-3

sₙ=n/2+(2a+(n-1)d)

s₂₅=25/2+(2 x 4+24 x -1)

25/2+(8+-24)

25/2+(-16)

25/2+-32/2

= -7/2

= - 3.5

Answered by Anonymous
11

 \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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