Question

finding AP 52 term of an ap is 29 and the 15 term of an ap is a 79 and find 55 term​

Answer 1

for ap tn formula is

Tn=a+(n-1)d

from first condition,

29=a+51d

And from second condition

79=a+14d

on solving both equation we get,

a=2579÷37 and d=-50÷37

now,

T55 term will be

T55=2579÷37+54×50÷37

=142.6756

Answer 2

Answer:

• 55th term is 25.01.

Step-by-step explanation:

Given:

• a₅₂ = 29
• a₁₅ = 79

To Find:

• a₅₅

Now, we know that,

⇒ a₅₂ = a + 51d  

⇒ 29 = a + 51 d      .........(1)

And,

⇒ a₁₅ = a + 14d  

⇒ 79 = a + 14d        ........(2)

Now, we will solve this equation by substitution method,

⇒ a + 51d = 29

⇒ a = 29 - 51d

Now put the value of 'a' in equation (2),

⇒ a + 14d = 79

⇒ 29 - 51d + 14d = 79

⇒ 29 - 37d = 79

⇒ -37d = 79 - 29

⇒ -37d = 50

⇒ d = 50/-37

⇒ d = - 1.35

Now, put the value of d in equation (1),

⇒ a + 51d = 29

⇒ a + 51(- 1.35) = 29

⇒ a - 68.91 = 29

⇒ a = 29 + 68.91

⇒ a = 97.91

Now, we will find 55th term,

⇒ aₙ = a + (n - 1)d

⇒ a₅₅ = 97.91 + (55 - 1)-1.35

⇒ a₅₅ = 97.91 - 74.25 + 1.35

⇒ a₅₅ = 97.91 - 72.9

⇒ a₅₅ = 25.01

Hence, 55th term is 25.01.

Now we will calculate A.P,

⇒ a₁ = 97.91

⇒ a₂ = 97.91 + (-1.35) = 96.56

⇒ a₃ = 97.91 + 2(-1.35) = 95.21

Hence, A.P is 97.91, 96.56, 95.21...............