If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is -3, find the 10th term

Solution:

Consider the first term and common difference of an AP are a and d.

From the question,

a₃ + a₈ = 7 and a₁₇ + a₁₄ = -3

a + (3 - 1)d + a + (8 - 1)d = 7

We know that an = a + (n- 1 )d

a + (7 - 1 )d + a + (14 - 1 )d = -3

a + 2d + a + 7d = 7

a + 6d + a + 13d = -3

2a + 9d = 7 ………….. (i)

2a + 19d = -3 …(ii)

By subtracting equation (i) from equation (ii),

10d = -10

d = -1

2a + 9(-1) = 7 [from equation (i)]

2a - 9 = 7

2a = 16

Dividing both sides by 2

a = 8

So we get

a₁₀ = a + (10 - 1)d

= 8 + 9(-1)

= 8 - 9

= -1

Therefore, the 10th term is -1.

✦ Try This: If sum of the 4rd and the 9th terms of an AP is 8 and the sum of the 8th and the 15th terms is -2, find the 12th term

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 15

If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is -3, find the 10th term

Summary:

If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is -3, the 10th term is -1

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