Question

Find the first term T1 and the common difference d of an AP whose 7th term is 88 and the 15th term is 160.

Answer 1

Answer:

T7=a+6d

T15=a+14d

a+6d=88--–-(1)

a+14d=160-----(2)

On solving:

d=9

evaluate the value of d in (1)

a+6×9=88

a+54=88

a=88-54

a=34.

Answer 2

Answer :

• First term = 34
• Common difference = 9

Step-by-step explanation :

we know that,

nth term of an A.P., is given by,

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

where

aₙ is the nth term

a is the first term

d is the common difference

• 7th term = 88

  a₇ = a + (7 - 1)d

  88 = a + 6d ---[1]

• 15th term = 160

  a₁₅ = a + (15 - 1)d

  160 = a + 14d ---[2]

Subtract equation [1] from equation [2]

160 - 88 = a + 14d - (a + 6d)

 72 = a + 14d - a - 6d

 8d = 72

   d = 72/8

   d = 9

common difference = 9

Substitute d = 9 in equation [1]

88 = a + 6d

88 = a + 6(9)

88 = a + 54

a = 88 - 54

a = 34

first term, T₁ = a = 34