Question

Calculate the difference between sum of first 20 term of arithmetic sequence, 6,10,14 and 15,19,23

Answer 1

Step-by-step explanation:

See photo post solution for details

Answer 2

Answer:

The difference between the sum of the first 20 terms of arithmetic sequence - 6,10,14 and 15,19,23 is 180

Step-by-step explanation:

• Calculating the sum of the first 20 terms of the series 6, 10, 14....

Sum of nth term = $\frac{n(2a + (n-1)d)}{2}$

Here, a = first term of AP, d = common difference, n = n terms of the AP.

Sum of the first series 6, 10, 14..............

a = 6, d = 4, n = 20

⇒ S(1) = $\frac{20(2 X 6 + (20-1)4)}{2}$

⇒ S(1) = 880

Sum of the second series 15, 19, 23.........

a = 15, d = 4, n = 20

⇒ S(2) = $\frac{20(2 X 15 + (20-1)4)}{2}$

⇒ S(2) = 1060

Now the difference is

⇒S(2) - S(1)

⇒1060 - 880

⇒180

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