Question

In arithmetic sequence common difference is 8 and 7th term is 45.
What is its 12th term ?
Find the position of 285 ?

Answer 1

Answer:

Hi ur answer is 12th term is 85 and 285 is 37th term

Answer 2

Given :-

common difference,d = 8

seventh term = 45

last term, an = 285

To find :-

Twelfth term

position of 285 term

We know that,

$a_7 = a + 6d = 45$

$\implies \: a + 6(8) = 45$

$\implies \: a = 45- 48$

$\implies \: a = -3 \dashleftarrow(1)$

Now it's 12th term,

$a_{12} = a + 11d$

$\implies \: - 3 + 11(8) \dashleftarrow(from \: 1)$

$\implies \: - 3 + 88$

$\implies \: \boxed{a_{12} = 85}$

Now the position of 285 will be

We know that,

$a_n = a + (n - 1)d$

$285 = - 3 + (n - 1)8$

$\frac{285 + 3}{8} = n - 1$

$\frac{288}{8} + 1 = n$

$n = \frac{288 + 8}{8}$

$n = \frac{296}{8}$

$\boxed{n = 37}$

Hence the position of 285 will be 37.