Question

how many terms of an A.P. 9,17,25......Must Be taken to give a sum of 636​

Answer 1

Answer:

there should be 12 terms to give a sum of 636.

Answer 2

Here,

AP : 9, 17, 25

So,

$\rm{} {\large{a}}_1 = 9 \\ \rm{}d = 8 \\ \rm{}S_n = 636$

We know,

$\bf{}S_n = \frac{1}{2} \{ 2a + (n - 1)d\} \\ \\ = > \frac{1}{2} \{ 2(9) + ( n- 1)8\} = 636 \\ \\ = > \frac{1}{2} \{ 18 + 8n - 8\} = 636 \\ \\ = > \frac{1}{2} \{10 + 8n \} = 636 \\ \\ \frac{\frac{1}{2} \{10 + 8n \}}{ \frac{1}{2} } = \frac{636}{ \frac{1}{2} } \\ \\ \\ = > 10 + 8n = 1272 \\ = > 8n = 1272 - 10 \\ = > 8n = 1262 \\ \\ = > \frac{8n}{8} = \frac{1262}{8} \\ \\ = > n = 157.75$

As,

• n is not a natural number, thus the given condition is not possible.

Hence,

• There exists no number of terms which will sum up to 636 in AP : 9, 17, 25