If the first term of an ap is 2 and the sum of the first five terms is equal to one forth of the sum of the next five terms, find the sum of the first 30 terms
Answers
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Answer:
The sum of first 30 terms is -2550
Step-by-step explanation:
Let the common difference of the AP be d.
ATQ,
Sum of first five terms = 1/4 ( sum of next five terms)
a1 + a2 + a3+ a4 + a5 = a6+a7+a8+a9+a10
N/2{2a + (n-1)d} = 1/4 [N/2{2a + (n-1)d}]
5/2 {2*2 + 4d} = 1/4 [ 5/2 {2*(a+5d) + 4d}]
5/2 {4+4d} = 1/4 [ 5/2 {2( 2+ 5d) +4d}]
10 + 10d = 1/4 [5/2 {4+10d+4d}
10 + 10d = 1/4 [10 + 35d]
10 +10d = 10/4 + 35d/4
35d/4 -10d = 10 - 10/4
35d/4 -40d/4 = 40/4 - 10/4
-5d/4 = 30/4
-5d = 30
d= -6
∴ the sum of first 30 terms are = 30/2 { 2*2 + 29*(-6)}
= 15 { 4 -174}
= 15(-170)
= - 2550