Question

If tnth = 3-4n, show that a1,a2,a3,.......Form an a.P. Also find s20.

Answer 1

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❄Question:-If an = 3 – 4n, then show that a1, a2, a3, … from an AP. Also, find S20.
❄Answer: -
Given that, nth term of the series is an = 3 - 4n
For a1,
Put n = 1 so a1 = 3 - 4(1) = - 1
For a2,
Put n = 2, so a1 = 3 - 4(2) = - 5
For a1,
Put n = 3 so a1 = 3 - 4(3) = - 9
For a1,
Put n = 4 so a1 = 3 - 4(4) = - 13
So AP is - 1, - 5, - 9, - 13, …
a2 - a1 = - 5 - (- 1) = - 4
a3 - a2 = - 9 - (- 5) = - 4
a4 - a3 = - 13 - (- 9) = - 4
Since, the each successive term of the series has the same difference. So, it forms an AP with common difference, d = - 4
We know that, sum of n terms of an AP is
Sn = n/2 {2a+(n-1) ×d}
Where a = first term
d = common difference
and n = no of terms
Then,
S20={20/2{2(-1) +(20-1)(-4) }
=10[ - 2 - 76]
= - 780
So Sum of first 20 terms of this AP is - 780.
HOPE IT HELPS YOU
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