Question

the sum of 2nd and 5th term of an ap is 23 the difference of the third term and the 10th term is 21 find the term to of AP​

Answer 1

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

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,

According to statement,

$\rm :\longmapsto\:a_2 + a_5 = 23$

$\rm :\longmapsto\:a + (2 - 1)d + a + (5 - 1)d = 23$

$\rm :\longmapsto\:2a + d + 4d = 23$

$\bf\implies \:2a + 5d = 23 - - - (1)$

Aɢᴀɪɴ,

According to statement,

$\rm :\longmapsto\:a_{10} - a_3 = 21$

$\rm :\longmapsto\:a + (10 - 1)d - (a + (3 - 1)d) = 21$

$\rm :\longmapsto\:a + 9d - (a + 2d) = 21$

$\rm :\longmapsto\:a + 9d - a - 2d= 21$

$\rm :\longmapsto\:7d = 21$

$\bf\implies \:d = 3$

On substituting d = 3, in equation (1), we get

$\rm :\longmapsto\:2a + 5 \times 3 = 23$

$\rm :\longmapsto\:2a + 15 = 23$

$\rm :\longmapsto\:2a = 23 - 15$

$\rm :\longmapsto\:2a = 8$

$\bf\implies \:a = 4$

Hence,

Required AP series is

$\rm :\longmapsto\:4, \: 7, \: 10, \: 13, \: - - - -$

Answer 2

Answer:

what to explained u r self