Question

If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.​

Answer 1

${\huge {\overbrace {\underbrace{\blue{ANSWER: }}}}}$

Given that,

3rd term, a3 = 4

and 9th term, a9 = −8

We know that,

an = a+(n−1)d

Therefore,

a3 = a+(3−1)d

4 = a+2d ……………………………………… (i)

a9 = a+(9−1)d

−8 = a+8d ………………………………………………… (ii)

On subtracting equation (i) from (ii),

we will get here,

−12 = 6d

d = −2

From equation (i),

we can write,

4 = a+2(−2)

4 = a−4

a = 8

Let nth term of this A.P. be zero.

an = a+(n−1)d

0 = 8+(n−1)(−2)

0 = 8−2n+2

2n = 10

n = 5

Hence, 5th term of this A.P. is 0.

Answer 2

$\sf\underline\red{Answer:-}$

$\sf\huge{Given} \begin{cases} \sf{3rd\:term(a_{3}) = 4} \\ \sf{ 9th\:term(a_{9}) = −8} \end{cases}$

We know that,

The nth term of AP is;

an = a + (n − 1) d

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Therefore,

$\sf\red{a_{3}}$ = a + (3 − 1) d

4 = a + 2d ……… (i)

$\sf\red{a_{9}}$ = a + (9 − 1) d

−8 = a + 8d ……… (ii)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

On subtracting equation (i) from (ii),

We will get here;

−12 = 6d

d = −2

From equation (i), we can write,

4 = a + 2 (−2)

4 = a − 4

a = 8

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Let nth term of this A.P. be zero.

$\sf\red{a_{n}}$ = a + (n − 1) d

0 = 8 + (n − 1) (−2)

0 = 8 − 2n + 2

$\sf\red{2_{n}}$ = 10

n = 5

Hence, 5th term of this A.P. is 0.