The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP

Solution:

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

From the question,

a₅ + a₇ = 52

a₁₀ = 46

a + (5 - l)d + a + (7 - 1)d = 52

We know that

a_n = a + (n- 1 )d]

a + (10 - 1 )d = 46

⇒ a + 4d + a + 6d = 52

Similarly a + 9d = 46

⇒ 2a + 10d = 52

and a + 9d = 46

⇒ a + 5d = 26 ………….. (i)

a + 9d = 46 ……………. (ii)

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

4d = 20

d = 5

From Equation (i)

a = 26 - 5(5) = 1

The required AP is a, a + d, a + 2d, a + 3d ….

i.e., 1, 1 + 5, 1 + 2(5), 1 + 3(5)…

i.e., 1, 6,11,16,….

Therefore, the AP is 1, 6, 11, 16, …..

✦ Try This: The sum of the 6th and the 8th terms of an AP is 32 and the 12th term is 36. Find the AP

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

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 7

Summary:

The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. The AP is 1, 6, 11, 16, …..

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