Question

find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22.

Answer 1

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Answer 2

hello users.....

we have given that
the second term of AP = 2
and
seventh term =22


we have to find
the sum of first 30 terms of an A.P.=?

solution:-
using formula:
An = a+(n-1) d

here ;
given that
a2 = 2 => a+d = 2 ....................(1)
&
a7= 22 => a+6d = 22....................(2)

solving (1)&(2) we get
(2-d) +6d = 22
=> 5d = 22-2= 20
=> d= 4
now put the value of d in (1) we get
a+4= 2
=> a= -2

now ,
using formula:
Sn = n/2{2a +(n-1) d}



the sum of first 30 terms of an A.P.=
here n= 30

=30/2 {2×(-2) +(30-1)×4}
= 15 {-4 +120 - 4}
= 15 × 112= 1680

hence ;
the sum of first 30 terms of an A.P.=1680 answer

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