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Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73 - Mathematics

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Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73

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Solution

Given that,

a11 = 38

a16 = 73

We know that,

an = a + (n − 1) d

a11 = a + (11 − 1) d

38 = a + 10d (1)

Similarly,

a16 = a + (16 − 1) d

73 = a + 15d (2)

On subtracting (1) from (2), we obtain

35 = 5d

d = 7

From equation (1),

38 = a + 10 × (7)

38 − 70 = a

a = −32

a31 = a + (31 − 1) d

= − 32 + 30 (7)

= − 32 + 210

= 178

Hence, 31st term is 178.

Concept: nth Term of an AP
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APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.2 | Q 7 | Page 106
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