Question

The 5th and 15th term of an A.p are 13and 17find that A.P

Answer 1

S O L U T I O N : (ques.error)

$\underline {\bf{Given\:: }}$

The 5th & 15th term of an A.P are 13 & -17.

$\underline {\bf{Explantion\::}}$

As we know that formula of an A.P;

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

• a is the first term.
• d is the common difference.
• n is the term of an A.P.

A/q

➠ a5 = 13

➠ a + (5 - 1)d = 13

➠ a + 4d = 13...............(1)

&

➠ a15 = -17

➠ a + (15 - 1)d = -17

➠ a + 14d = -17.........…...(2)

Now, using by substitution method :

From equation (1), we get;

➠ a + 4d = 13

➠ a = 13 - 4d.............(3)

Therefore, putting the value of a in equation (2),we get;

➠ 13 - 4d + 14d = -17

➠ 13 + 10d = -17

➠ 10d = -17 - 13

➠ 10d = -30

➠ d = -30/10

➠ d = -3

Therefore, putting the value of d in equation (3),we get;

➠ a = 13 - 4 × (-3)

➠ a = 13 - (-12)

➠ a = 13 + 12

➠ a = 25

Now,

The arithmetic progression :

• a = 25
• a + d = 25 + (-3) = 25 - 3 = 22
• a + 2d = 25 + 2(-3) = 25 +(-6) = 25 - 6 = 19
• a + 3d = 25 + 3(-3) = 25 + (-9) = 25 - 9 = 16

Thus,

The AP will be 25, 22, 19, 16....

Answer 2

Answer:

S O L U T I O N : (ques.error)

Given:

The 5th & 15th term of an A.P are 13 & -17.

Explantion:

As we know that formula of an A.P;

a

n

=a+(n−1)d

a is the first term.

d is the common difference.

n is the term of an A.P.

A/q

➠ a5 = 13

➠ a + (5 - 1)d = 13

➠ a + 4d = 13...............(1)

&

➠ a15 = -17

➠ a + (15 - 1)d = -17

➠ a + 14d = -17.........…...(2)

Now, using by substitution method :

From equation (1), we get;

➠ a + 4d = 13

➠ a = 13 - 4d.............(3)

Therefore, putting the value of a in equation (2),we get;

➠ 13 - 4d + 14d = -17

➠ 13 + 10d = -17

➠ 10d = -17 - 13

➠ 10d = -30

➠ d = -30/10

➠ d = -3

Therefore, putting the value of d in equation (3),we get;

➠ a = 13 - 4 × (-3)

➠ a = 13 - (-12)

➠ a = 13 + 12

➠ a = 25

Now,

The arithmetic progression :

a = 25

a + d = 25 + (-3) = 25 - 3 = 22

a + 2d = 25 + 2(-3) = 25 +(-6) = 25 - 6 = 19

a + 3d = 25 + 3(-3) = 25 + (-9) = 25 - 9 = 16

Thus,

The AP will be 25, 22, 19, 16....