Question

Arithmetic progression question

Answer 1

Hi ,

i ) 63 + 65 + 67 + ...

first term = a = 63

Common difference = d

d = a2 - a1 = 65 - 63 = 2

mth term = am = a + ( m - 1 ) d

= 63 + ( m - 1 ) 2

= 63 + 2m - 2

= 61 + 2m ---( 1 )

ii ) 3 + 10 + 17 + ...

a = 3 ,

d = 10 - 3 = 7

am = 3 + ( m - 1 )7

= 3 + 7m - 7

= 7m - 4 ---( 2 )

According to the problem given ,

( 1 ) = ( 2 )

61 + 2m = 7m - 4

61 + 4 = 7m - 2m

65 = 5m

65/5 = m

13 = m

Therefore ,

m = 13

Option ( C ) is correct.

I hope this helps you.

: )

Answer 2

1st Series,

63 + 65 + 67 + 69 + ...

$\bf \: a_{1} = 63 \\ \bf \: a_{2} = 65 \\ \\ d = a_{2} - a_{1} \\ d = 65 - 63 \\ \bf \: d = 2$

2nd Series,

3 + 10 + 17 + 24 + ...

$\bf \: a_{ 1} = 3 \\ \bf \: a_{2} = 10 \\ \\ d = a_{2} - a_{1} \\ d = 10 - 3 \\ \bf \: d = 7$

Since, it is given that the mth term of both the AP is equal,

$a + (m - 1)d = a + (m - 1)d \\ \\ 63 + (m - 1)2 = 3 + (m - 1)7 \\ \\ 63 + 2m - 2 = 3 + 7m - 7 \\ \\ 61 + 2m = - 4 + 7m \\ \\ 61 + 4 = 7m - 2m \\ \\ 5m = 65 \\ \\ m = \frac{5(13)}{5} \\ \\ \bf \: m = 13$

So, the correct option is (c)

If any doubt, please ask ;)