Math, asked by katestyle, 9 days ago

Find the nth term and sum up to 13 terms of the sequence: 3,−1, 1/3, -1/9....​

Answers

Answered by BʀᴀɪɴʟʏAʙCᴅ
0

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, \sf{a_n~=~A_n~+~b}

→ 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,

\longrightarrow~\sf{S_n~=~\dfrac{n~(a~+~l)}{2}}

Where,

  • a = the first term

  • l = the last term

Putting “n = 1” in the given \sf{a_n} we get,

→ a = A(1) + B = A + B

For the last term (l), here n = 20

→ A₂₀ = A(20) + B = 20A + B

→ S₂₀ = \sf{\dfrac{20}{2}~\bigg((A~+~B)~+~20A~+~B\bigg)}

→ 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).

Answered by hmnagaraja3
0

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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