Find the nth term and sum up to 13 terms of the sequence: 3,−1, 1/3, -1/9....
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Q. Find the nth term and sum up to 13 terms of the sequence: 3,−1, 1/3, -1/9....
Answer :
Given,
An A.P. whose nth term is given by,
→ We need to find the sum of first 20 terms.
To find the sum of the n terms of the given A.P.,
we use the formula,
Where,
- a = the first term
- l = the last term
Putting “n = 1” in the given we get,
→ a = A(1) + B = A + B
For the last term (l), here n = 20
→ A₂₀ = A(20) + B = 20A + B
→ S₂₀ =
→ S₂₀ = 10 [21A + 2B]
→ S₂₀ = 210 A + 20B
Therefore, the sum of the first 20 terms of the given A.P. is (210 A + 20B).
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Answer:
Given sequence is 3,1,−1,−3,…..
Now,
1–3=−1–1=−3–(−1)=−2
Thus, the given sequence is an A.P. where a=3 and d=−2.
So, the general term of the A.P is given by
t
n
=a+(n–1)d
=3+(n–1)(−2)
=3–2n+2
=5–2n
Therefore, the 23rd term =t
23
=5–2(23)=5–46=−41
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