2) The 6 th term of an A.P is 80 and its 15 th term is 16. Find the fi

1.	2) The 6 th term of an A.P is 80 and its 15 th term is 16. Find the first 3terms of the AP
Answer» Answer : The FIRST three terms are $\bf \frac{1040}{9},\frac{976}{9} ,\frac{912}{9}$ Step-by-step explanation : Given, 6th term = 80 15th term = 16 To find, first 3 terms Solution, we know, nth term of A.P. is given by, $\boxed{\bf a_n=a+(n-1)d}$ where a is the first term d is the common difference aₙ is the nth term 6th term = 80 a₆ = a + (6 - 1)d 80 = a + 5d --- [1] 15th term = 16 a₁₅ = a + (15 - 1)d 16 = a + 14d --- [2] Subtract equation [1] from equation [2], 16 - 80 = a + 14d - (a + 5d) - 64 = a + 14d - a - 5d - 64 = 9d d = -64/9 ⇒ common difference = -64/9 Substitute d = -64/9 in equation [1] 80 = a + 5d 80 = a + 5(-64/9) 80 = a - (320/9) a = 80 + (320/9) a = (720+320)/9 a = 1040/9 first term, a = 1040/9 second term, a₂ = a + d a₂ = 1040/9 + (-64/9) a₂ = (1040-64)/9 a₂ = 976/9 third term, a₃ = a₂ + d a₃ = 976/9 + (-64/9) a₃ = (976-64)/9 a₃ = 912/9

2) The 6 th term of an A.P is 80 and its 15 th term is 16. Find the first 3terms of the AP

Answer»

Answer :

The FIRST three terms are $\bf \frac{1040}{9},\frac{976}{9} ,\frac{912}{9}$

Step-by-step explanation :

Given,

6th term = 80
15th term = 16

To find,

first 3 terms

Solution,

we know,

nth term of A.P. is given by,

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

where

a is the first term

d is the common difference

aₙ is the nth term

6th term = 80

a₆ = a + (6 - 1)d

80 = a + 5d --- [1]

15th term = 16

a₁₅ = a + (15 - 1)d

16 = a + 14d --- [2]

Subtract equation [1] from equation [2],

16 - 80 = a + 14d - (a + 5d)

- 64 = a + 14d - a - 5d

- 64 = 9d

d = -64/9

⇒ common difference = -64/9

Substitute d = -64/9 in equation [1]

80 = a + 5d

80 = a + 5(-64/9)

80 = a - (320/9)

a = 80 + (320/9)

a = (720+320)/9

a = 1040/9

first term,

a = 1040/9

second term,

a₂ = a + d

a₂ = 1040/9 + (-64/9)

a₂ = (1040-64)/9

a₂ = 976/9

third term,

a₃ = a₂ + d

a₃ = 976/9 + (-64/9)

a₃ = (976-64)/9

a₃ = 912/9