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Answer:
AnswEr :
Remeber – To Calculate the nth term of an AP formula is Given by » aₙ = a + (n – 1)d «
where,
a = First Term
n = n term
d = Common difference
Let the Common difference of the AP be d. We're provided with First Term of Both AP's 3 and 8. We're asked to find out the difference b/w their 2nd and 20th term.
⠀
\begin{gathered}:\implies\sf a_n = \Big[3 + (n - 1)d\Big] \;and, \;b_n = \Big[8 + (n - 1)d\Big]\\\\\end{gathered}
:⟹a
n
=[3+(n−1)d]and,b
n
=[8+(n−1)d]
\begin{gathered}:\implies\sf a_n - b_n = \Big[3 + (n - 1)d\Big] - \Big[8 + (n - 1)d\Big] \\\\\end{gathered}
:⟹a
n
−b
n
=[3+(n−1)d]−[8+(n−1)d]
\begin{gathered}:\implies\sf a_n - b_n = 3 + \cancel{(n - 1)d} - 8 - \cancel{(n - 1)d} \\\\\end{gathered}
:⟹a
n
−b
n
=3+
(n−1)d
−8−
(n−1)d
\begin{gathered}:\implies\sf a_n - b_n = 3 - 8 \\\\\end{gathered}
:⟹a
n
−b
n
=3−8
\begin{gathered}:\implies{\pmb{\bf{ a_n - b_n = - 5}}}\\\\\end{gathered}
:⟹
a
n
−b
n
=−5
a
n
−b
n
=−5
\therefore∴ Hence, Difference b/w their 2nd and 20th term is – 5.
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