Question

sum of 6th and 9th term of an A.P is 101 and sum of 10th and 16th term is 178.find the first 3-terms of the A.P

Answer 1

Go through it thoroughly and ask if you have any doubt at any step.
Hope this helps.

Answer 2

The first three terms are 5, 12 and 19

Given:

The sum of the 6th and 9th terms of an A.P is 101

The sum of the 10th and 16th terms is 178

Find:

The first 3-terms of the A.P

Solution:

a₆+a₉ = 101

a+ 5d + a+8d = 101

2a+ 13d = 101       (1)

a₁₀ + a₁₆ = 178

a + 9d+ a+15d  = 178

2a+24d = 178

or

a+12d = 89         (2)

(1) - (2) = a+d = 12

or a = 12-d        (3)

Substitute (3) in (2)

a +12d = 89

12-d+12d = 89

d = 7         (4)

Substitute (4) in (2)

a+ 12d = 89

a+ (12*7) = 89

a = 5

a1 = 5

a₂ = 5+d = 5+ 7 = 12

a₃ = 5+ 2d = 5+ (2*7)

    = 5+14 = 19

So the first three terms are 5, 12 and 19

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