Question

if tn represents nth term of an AP, t2+t5-t3=10 and t2+t9= 17, find its first term and its common difference

Answer 1

Answer:

The common difference is -1

Step-by-step explanation:

T₂ ₊ T₅ ₋ T₃ = 10...........(1)

T₂ + T₉ = 17...................(2)

Tn = a + (n-1)d

(1),

  a + d + a + 4d -a -2d = 10

a + 3d = 10...................(3)

(2),

   a + d + a + 8d =17

 2a + 9d = 17.........................(4)

Solving (3) and (4),

                             2a + 9[ 10 - a]/3

                             2a + 30 - 3a = 17

                            a = 30 - 17

                            a = 13...................(5)

put (5) in(1),

                  13 + 3d = 10

                     3d = -3

                        d = -1

Answer 2

• First term = 13

• Common difference = - 1

Step-by-step explanation:

Let a be the first term of the AP and d be the common difference.

Given that,

t2 + t5 - t3 = 10

or, (a + d) + (a + 4d) - (a + 2d) = 10

or, a + 3d = 10 ..... (1)

and t2 + t9 = 17

or, (a + d) + (a + 8d) = 17

or, 2a + 9d = 17 ..... (2)

From (1), we get a = 10 - 3d and substituting this value in (2), we get

2 (10 - 3d) + 9d = 17

or, 20 - 6d + 9d = 17

or, 3d = - 3

or, d = - 1

Then a = 10 - 3 (- 1) = 10 + 3 = 13

Therefore the first term is 13 and the common difference is - 1.

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