Question

find the sum of arithmetic progression
8,3,-2 ,.........up to 22 terms


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Answer 1

${\Green{\hug{Hey!!}}}$

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${\underline{\bold{Given:-}}}$

a=8

n=22

d=-5

S22=22/2{2*8+21*-5}

=11(16-105)

=-979

${\boxed{\red{-979}}}$

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${\red{\huge{Thanks}}}$

Answer 2

ANSWER :

1, 4, 7, 10 ,13 etc.....are called sequence of an A.P ( arithmetic progression ).

• 1st term   : a = a₁ = 1

• 2nd term : a₂ = 4 = ( 1 + 3 ) = a + d
• Common difference ( d ) : a₂ - a₁
• 3rd term : a₃ = a + 2d

General Formula of an A.P : an = a + ( n - 1 ) d

( an = last term )

For finding sum of the A.P we have another formula :

• Sn = n/2 [ 2a + ( n - 1 ) d

( Sn donates : Sum of the A.P )

→ GIVEN A.P =  8,3,-2 ,.........up to 22

a = 8 ( first term of an Ap )

d = a₂ - a₁ = 3 - 8

= - 5  (Common Difference of the given AP )

n = 22  ( last term )

Now we have to Put these values in the formula :

• Sn = n/2 [ 2a + ( n - 1 ) d

S₂₂ =  22 / 2 [ 2 × 8 + ( 22 - 1 ) ( ₋ 5 )

S₂₂ =  11 [ 16 + ( 21 ) ( - 5 ) ]

S₂₂ =  11 [ 16 - 105 ]

S₂₂ =  11 [ ₋ 89 ]

S₂₂ =  ₋ 979

∴ The sum of arithmetic progression  8,3,-2 ,.........up to 22 terms is

• S₂₂ =  ₋ 979