Question

Find the missing term (?) of the following, given that 'a' is the
first term, d the common difference, a, the nth term of the AP.
(iii) a = ?, d = -3, n = 18, an = -5
(iv) a = -18.9, d = 2.5, n = ?, an = 3.6
(v) a = 3.5, d = 0, n = 105, an = ?

Urgent pls ​

Answer 1

Question

Find the missing term (?) of the following, given that 'a' is the  first term, d the common difference, a, the nth term of the AP.

(iii) a = ?, d = -3, n = 18, an = -5

(iv) a = -18.9, d = 2.5, n = ?, an = 3.6

(v) a = 3.5, d = 0, n = 105, an = ?

Solution

(iii) We know,

$\sf{a_n=a+(n-1)d}\\\\\sf{\longrightarrow -5=a+(18-1)-3}\\\\\sf{\longrightarrow -5=a-51}\\\\\sf{\longrightarrow a=-5+51}\\\\\sf{\longrightarrow a=49}$

$\rule{120}2$

(iv) We know,

$\sf{a_n=a+(n-1)d}\\\\\sf{\longrightarrow 3.6=-18.9+(n-1)2.5}\\\\\sf{\longrightarrow 3.6=-18.9+2.5n-2.5}\\\\\sf{\longrightarrow 22.5+2.5=2.5n}\\\\\sf{\longrightarrow 25=2.5n}\\\\\sf{\longrightarrow n=10}$

$\rule{120}2$

(v) We know,

$\sf{a_n=a+(n-1)d}\\\\\sf{\longrightarrow a_n=3.5+(105-1)0}\\\\\sf{\longrightarrow a_n=3.5+104 \times 0}\\\\\sf{\longrightarrow a_n=3.5}$

Answer 2

$\pink{\bf{\underline{Given:-}}}$

(i) a = ?, d = -3, n = 18, $a_{n}$ = -5

(ii) a = -18.9, d = 2.5, n = ?, $a_{n}$ = 3.6

(iii) a = 3.5, d = 0, n = 105, $a_{n}$ = ?

Here, In AP :-

▪'a' is the 1ˢᵗ term

▪'d' is the common difference

▪'$a_{n}$' is the nᵗʰ term

$\purple{\bf{\underline{To\:Find:-}}}$

(i) a = ?

(ii) n = ?

(iii) $a_{n}$ = ?

$\huge\red{\bf{\underline{Solution:-}}}$

We know that,

$\blue{\boxed {\boxed {a_{n} = a + (n-1)d}}}$

(i)

$a_{ (- 5)} = a + (18 - 1) \times ( - 3)$

$⟾ - 5 = a + 17 \times ( - 3)$

$⟾ - 5 = a - 51$

$⟾ \: a = 51 - 5$

$⟾ \: a = 46$

$\bold\green{\bf{Hence,\:the\:value\:of\:a\:is\:46}}$

___________________________________

(ii)

$a_{3.6} = - 18.9 + (n - 1) 2.5$

$⟾ \: 3.6 = - 18.9 + 2.5n - 2.5$

$⟾ \: 3.6 = 2.5n - 21.4$

$⟾ \: 3.6 + 21.4 = 2.5n$

$⟾ \: 25 = 2.5n$

$⟾ \: n = \frac{25}{2.5}$

$⟾ \: n = 10$

$\bold\green{\bf{Hence,\:the\:value\:of\:n\:is\:10.}}$

_____________________________________

(iii)

$a_{n} = 3.5 + (105 - 1) \times 0$

$⟾ \: a_{n} = 3.5$

$\bold\green{\bf{Hence,\:the\:value\:of\:a_{n}\:is\:3.5}}$