Question

find the sum of the first 22 terms of the AP:8,3,-2,

Answer 1

Hey there

here is the answer to your dilemma

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Given terms of the AP are :- 8 , 3 , -2

a = a1 = 8

d = a2 - a1

d = 3 - 8

d = -5

*Sum of the terms in an ap is followed by a formula as follow*

$sn = \frac{n}{2} (2 a+ (n - 1)d)$
here

n = number of terms = 22

a = 8

d = (-5)

» Substituting the values in the formula

» s22 = 22/2 [ 2 × 8 + ( 22 - 1 ) -5 ]

» s22 = 22/2 [ 16 + ( 21 ) -5 ]

» s22 =22/2 [ 16 + 21 × -5 ]

» s22 = 22/2 [ 16 + (- 105 ) ]

» s22 = 22/2 [ 16 - 105 ]

» s22 = 22/2 [ - 89 ]

» s22 = 11 × (-89)

» s22 = ( -979 )

_* therefore sum of 22 terms in the given ap is - 979 *_

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thnq !!

Answer 2

Your answer starts from here :

8,3,......

Here, a = 8 , d = 3-8 = -5 and n = 22

We know that :

Sn = n/2 { 2a + ( n - 1 ) d }

Therefore,

S₂₂ = 22/2 { 16 + 21 ( - 5 ) }

S₂₂ = 11 ( 16 - 105 )

S₂₂ = 11 ( - 89 )

S₂₂ = - 979

Hence, the sum of first 22 terms of the AP is - 979.