Question

Q.1.find the middle terms of AP 1,8,15....505

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Answer 1

Answer:

253

Step-by-step explanation:

505=1+(n-1)7

505=1+7n-7

505=7n-6

511=7n

n=73

middle term=73+1/2

=37

hence the term is

1+(37-1)7

253

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Answer 2

$\bigstar\:\:\underline{\sf AnsWer :} \bigstar$

For given AP,

First term, a = 1

Common difference,

$\sf \: d = a_2 – a$

$\sf \: = 8 – 1$

$\sf = 7$

Let the number of terms be n, then

Last term, an = 505

★ We know, nth term of an AP is

$\sf \: a_n = a + (n – 1)d$

$\sf \: ⇒ 505 = 1 + (n – 1)7$

$\sf⇒ 504 = 7(n – 1)$

$\sf⇒ n – 1 = 72$

$\sf⇒ n = 72 - 1$

$\sf⇒ n = 73$

The middle term of A.P.

$\sf = \frac{73 + 1}{2} = {37}^{th} term$

Also,

$\sf \: a_{37} = a + 36d$

$\sf \: = 1 + 36(7)$

$\sf \: = 1 + 252$

$\bf{= 253}$