Question

If the 17th term of Ap is -6 and the common difference is -2, find the sum of it's first 20 terms.
PLS REPLYY FASTT​

Answer 1

Answer:

I don't know

Step-by-step explanation:

sorry bye bye take care

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ 17th term of an AP series is - 6 and common difference is- 2.

Let assume that

↝ First term of an AP series is a

and

↝ Common difference of an AP is d

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

aₙ is the nᵗʰ term.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

Tʜᴜs,

$\rm :\longmapsto\:a_{17}\:=\:a\:+\:(17\:-\:1)\:d$

$\rm :\longmapsto\:a_{17}\:=\:a\:+\:16d$

On substituting the values, we get

$\rm :\longmapsto\: - 6 = a + 16( - 2)$

$\rm :\longmapsto\: - 6 = a - 32$

$\rm :\longmapsto\: 32- 6 = a$

$\bf\implies \:a = 26$

Now, we have

$\rm :\longmapsto\:a = 26$

$\rm :\longmapsto\:d = - \: 2$

$\rm :\longmapsto\:n = 20$

Now,

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Sum of n  terms of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

Sₙ is the sum of n terms of AP.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

On substituting the values, we get

$\rm :\longmapsto\:S_{20}\:=\dfrac{20}{2} \bigg(2 \:(26)\:+\:(20\:-\:1)\:( - 2) \bigg)$

$\rm :\longmapsto\:S_{20}\:=10 \bigg( \:52\: - \:38 \bigg)$

$\rm :\longmapsto\:S_{20}\:=10 \bigg( \:14 \bigg)$

$\rm :\longmapsto\:S_{20}\:= \: 140$