# 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. - Mathematics

Sum

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

Let the first term and common difference of an AP are a and d, respectively.

a3 + a8 = 7 and a17 + a14 = -3

⇒ a + (3 – 1)d + a + (8 – 1)d = 7   .......[∵ an = a + (n- 1 )d]

and a + (7 – 1 )d + a + (14 – 1 )d = – 3

⇒ a + 2d + a + 7d = 7

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

⇒ 2A + 9d = 7  .......(i)

And 2a + 19d = – 3 ......(ii)

On subtracting equation (i) from equation (ii), we get

10d = – 10

⇒ d = – 1

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

⇒ 2a – 9 = 7

⇒ 2a = 16

⇒ a = 8

∴ a10 = a + (10 – 1)d

= 8 + 9(–1)

= 8 – 9

= –1

Concept: Sum of First n Terms of an A.P.
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.3 | Q 15 | Page 53
Share