Math, asked by knavdeep1702, 1 year ago

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find the sum of the first 25 terms of an ap whose nth term is given by tn=2-3n...

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Answered by shadowsabers03

The question is to find the sum of first 25 terms.

Given that T_n = 2 - 3n.

So first let me find the 13th term. (You'll get it later why I'm finding 13th term.)

T₁₃ = 2 - 3 × 13

T₁₃ = 2 - 39

T₁₃ = - 37

Okay, let's find the sum.

$S_{25}=25\times [\frac{25+1}{2}]^{th}\ $term$ \\ \\ S_{25}=25 \times 13^{th}\ $term$ \\ \\ S_{25}=25\times -37 \\ \\ S_{25}=\bold{-925}$

∴ The answer is -925.

We can find it by this simple method, and there's no need to find those like first term, 25th term, common difference, etc.

Thank you. Have a nice day. :-))

#adithyasajeevan

shadowsabers03: In this question, as 25 is an od number, we can take n = 25.

shadowsabers03: So [(n + 1) / 2]th term = [(25 + 1) / 2]th term = [26 / 2]th term = 13th term

shadowsabers03: So we can find the sum of first 25 terms of the AP by multiplying 25 by the 13th term. For this, I've found 13th term.

knavdeep1702: ohkay

knavdeep1702: thanks a lot now i got it

shadowsabers03: That method will be helpful for such questions.

shadowsabers03: You're welcome.

shadowsabers03: Among the 25 terms, 13th term can be said as average. We had learnt that average multiplied by no. of terms gives sum, hadn't we?

knavdeep1702: yup

shadowsabers03: Mmm

Answered by saravjit1974

Answer:

Step-by-step explanation:

an = 2-3n

Let n =1

a1 = 2-3= -1

Let n=2

a2 = 2-6 = -4

d = -4+1=-3

Sn =n/2(2a+(n-1)d)

S25 = 25/2 (-2+(25-1)-3)

S25 = 25/2 (-2+(-72))

S25 = 25/2*-74

S25. = -925

I hope it will help you..

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