the sum of first n term of ap is 4nsquare+2n. find its nth term of this ap
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Substitute n = 1 in (1), we get
sn = 4(1)^2 + 2(1)
= 4 + 2
= 6.
So, Sum of the first term of AP is 6 i.e a = 6.
Now,
Substitute n = 2 in (1), we get
sn = 4(2)^2 + 2(2)
= 4 * 4 + 2 * 2
= 16 + 4
= 20.
So, Sum of the first 2 terms = 20.
Now,
First-term + second term = 20
6 + a2 = 20
a2 = 20 - 6
a2 = 4.
Hence in AP,
first term a = 6.
common difference d = a2 - a1
= 14 - 6
= 8.
We know that sum of n terms of an AP an = a + (n - 1) * d
= 6 + (n - 1) * (8)
= 6 + 8n - 8
= 8n - 2.
Therefore the nth term of the AP = 8n - 2 (or) 2(4n - 1).
Hope this helps!
Answer:
Step-by-step explanation: