Question

For what value of m are the mth term s of the following two A.p.'s the same

Answer 1

Step-by-step explanation:

Given:

Two A.P.s

(I) 1,3,5,7...

(ii)4,8,12,16...

To find:For what value of m are the mth term s of the following two A.p.'s the same

Solution:

We know that general term of AP is given by

$\boxed{\blue{\bold{a_n = a + (n - 1)d}}}$

In first AP: First term a1 = 1

Common difference d1= 2

In second AP: First term a2 = 4

Common difference d2= 4

Since mth terms of both AP are same

$a_{m1} = a_{m2} \\ \\ a_1 + (m - 1)d_1 = a_2 + (m - 1)d_2 \\ \\ 1 + (m - 1)(2) = 4 + (m - 1)(4) \\ \\ 2(m - 1) - 4(m - 1) = 4 - 1 \\ \\ - 2(m - 1) = 3 \\ \\ 2(m - 1) = - 3 \\\\ (m - 1) = \frac{ - 3}{2} \\ \\ m = \frac{ - 3}{2} + 1 \\ \\ m = \frac{ - 3 + 2}{2} \\ \\\bold{ m = \frac{ - 1}{2}}$

As,

Number of terms of an AP are positive integers .

here m= -0.5,

Thus,

No such m exist for which mth terms of both the A.P.'s are equal.

Hope it helps you.

To learn more on brainly:

1)find the 60th term of the AP 8,10,12,if it has a total of 60 terms and hence find the sum of its last ten terms?

https://brainly.in/question/304224

Answer 2

Answer:

Number of terms of an AP are positive integers .

Number of terms of an AP are positive integers .here m= -0.5,

Number of terms of an AP are positive integers .here m= -0.5,Thus,

Number of terms of an AP are positive integers .here m= -0.5,Thus,No such m exist for which mth terms of both the A.P.'s are equal.