Question

Please answer my question

Answer 1

Question :-

Determine the AP whose third term is 16 and the 7th term exceed the 5th term by 12.

Solution :-

As given

a₃ = 16

→ a + 2 d = 16

→ a = 16 - 2 d   ..... eqn (1)

Also given

a₅ + 12 = a₇

→( a + 4 d)+ 12 = a + 6 d

→ a + 4 d + 12 - a - 6 d = 0

→ 12 - 2 d = 0

→ 2 d = 12

→ d = 6

putting value of d in eqn (1)

a = 16 - 2 d

a = 16 - 2 ( 6 )

a = 16 - 12

→ a = 4

Hence the required A.P is

a , a + d , a + 2 d ......

4 , 10 , 16 ....   ( Ans. )

Answer 2

{4, 10, 16, 22 • • •}

Step-by-step explanation:

Given:

3rd term = 16

7th term = 5th term + 12

To Determine:

The A.P

Solution:

let, The 1st term be a and common differences be d.

$\textsf{So,} \: \: a_5 =a + 4d \: \: \: and \: \: \: a_7 = a + 6d$

According to question,

$a_7 = a_5 +12 \\ \\ a + 6d = a + 4d +12\\ \\ \cancel{a} + 6d - 4d = \cancel{a} + 12\\ \\ 2d = 12 \\ \\ \boxed{d = 6}$

So, The common differences is 6.

Again,

$a_3 = a + 2d \\ \\ 16 = a + 2.6 \\ \\ 16 = a + 12 \\ \\ a = 16 - 12 \\ \\ a = 4$

Hence, The first term is 4 and common differences is 6.

Now, A.P = {4, 10 , 16, 22 • • •}

Additional Information

Arithmetic Progression (A.P) = An arithmetic progression is a sequence of a number in which the consecutive terms are formed by adding a constant quantity with the preceding term. The constant quantity is known the common difference of the progression. From the definition it is clear that an arithmetic progression is a sequence of number in which the difference between any two consecutive terms is constant.

e.g The sequence {4, 7, 10, 13, • • •} is an A.P whose common difference is 3, since

2nd term(7) - 1st term(4) = 3

3rd term(10) - 2nd term(7) = 3

4th term(13) - 3rd term(10) = 3

constant.