calculate the difference between the sums of the first 20 terms of the arthmetic sequence 6, 10, 14..... and 15, 19, 23.....
Answers
Answer:
it is 8 hope it helps u
Step-by-step explanation:
Answer:
Sequenceis6,10,14…
It is an A.P
Herea1=6,d=4
Tofindout20thterm ,(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
21thtermisa21=a20+d=82+4=86
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
Shubham:)
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Carl Bryan, B.S. Mathematics, Carnegie Mellon University (1972)
Answered May 4, 2018 · Author has 4.2K answers and 1.5M answer views
Term 1 is 6. The difference is 4. Term 20 is 6 + 19 x 4 = 82. Term 21 is 86. Term 40 is 6 + 39 x 4 = 162.
The sum of the first 20 terms is 20/2 (6 + 82) = 880.
The sum of the next 20 terms is 20/2 (86 + 162) = 2480.
The difference of the sums is 2480 - 880 = 1600.
Alternately the sum of all 40 terms is 40/2 (6 + 162) = 3360.
The sum of the second 20 terms is 3360 - 880 = 2480.
The difference is still 2480 - 880 = 1600.
Step-by-step explanation: