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

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

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  1. 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=24/5

    We 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=90

    Hence,the sum of first six terms is 90.

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