calculate the difference between the sum of the first 20 term of the arethametic sequence 6, 10, 14...and 15, 19, 23...
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What is the difference between the sum of the first 20 terms and the next 20 terms of the arithmetic sequence 6,10,14…?
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Sequenceis6,10,14…
It is an A.P
Herea1=6,d=4
To find out 20th term, (n=20)
a20=a1+(20−1)d
a20=6+(20−1)4
a20=6+(20−1)4
a20=6+(20−1)4
a20=6+76
a20=82
Sum of first 20 terms
s20=n(a1+a20)/2
s20=20(6+82)/2
s20=(20×88)/2
s20=880 ft
To find out sum of last 40 term ,we have to find 40th term,
a40=6+(40–1)4
a40=6+39×4
a40=6+156
a40=162
Sum of next 20 terms (from 21st to 40th)
sum=n(a21+a40)/2
sum=20(86+162)/2
sum=(20×248)/2
sum=2480
Therefore difference between sum of last 20 and first 20 terms in the given series
=2480
=1600
Answer is 1600
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