Question

Find the sum of:-
50,46,42.....to 10 terms

Answer 1

A.P. : 50, 46, 42 .....

First term, $\sf{a}$ = 50

Second term, $\sf{a_2}$ = 46

Common difference, d = $\sf{a_2 - a}$

d = 46 - 50 = - 4

Now,

$\sf{a_n = a + (n - 1)d}$

n = 10

$\sf{a_{10} = 50 + (10 - 1)(- 4)}$

$\sf{a_{10} = 50 - 36}$

$\sf{a_{10} = 14}$

Now,

$\sf{S_n = {\dfrac{n}{2}} (a + a_n)}$

n = 10

$\sf{S_{10} = {\dfrac{10}{2}} (50 + 14)}$

$\sf{S_{10} = 5 (64)}$

$\large\sf{S_{10} = 320}$

Answer 2

a = 50
d = -4
n = 10

an = a+ (n-1) d

a10 = a+ 9d

a10 = 50 + 9 (-4)

a10 = 50 + (-36)

a10 = 50- 36

a10 = 14

a10 = l

S = n÷2 { a + l}

S = 10 ÷ 2 { 50 + 14 }

S = 5 { 64 }

S = 320

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