if the first term of an AP is 2 and sum of first 5 terms is equal to one fourth of the sum of next five terms find S30
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Step-by-step explanation:
Nice one. First of all let's write all given situations. For this A.P. :-
a = 2 and S5 = (S10-S5)/4
Lete explain the second one. The sum of first 5 terms is S5 and sum of first 10 terms is S10. So, sum of next 5 terms ( i.e sum of 6th to 10th term ) is S10 - S5.
So, from this equation we get 5S5 = S10
and Sn = n/2 ( 2a + (n-1)d )
So, S5 = 5/2( 4 + 4d )
or S5 = 2.5×4(1+d) = 10(1+d)
And S10 = 10/2( 4+ 9d ) = 5(4+9d )
So, 50(1+d) = 5(4+9d)
10 + 10d = 4 + 9d
d = -6
So, Sum of first 30 terms = S30
= 30/2(4+29d)
=15(4–174)
= 15(-170)
= -255
So, required answer is -255
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