if a=3 and t6=27,find the sum of the first six terms of the A. P.

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if a=3 and t6=27,find the sum of the first six terms of the A. P.

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## Given

first term(a)= 3

t₆= 27

## To Find

we have to find first six terms of the A.P

[tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex]

first term (a)= 3

t₆= 27

t₆ can be written as : a+5d

↣a+5d= 27

put the value of a

↣3+5d= 27

↣5d= 27-3

↣5d= 24

↣

d=24/5We have to find sum of first six terms

Sₙ=n/2 [2a+(n-1)d]↣S₆= 6/2[2(3)+(6-1)24/5]

↣S₆= 3[6+5×24/5]

↣S₆=3[6+24]

↣S₆= 3(30)

↣S₆=90Hence,the sum of first six terms is 90.