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The 9th term of an AP is 499 and 499th term is 9. The term which is equal to zero is
CBSE class-10 math arithmetic-progression A.P
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The 9th term of an AP is 499 and 499th term is 9. The term which is equal to zero is

(a) t508 (b) t805 (c) t504 (d) t501 

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james_mark
Asked by james_markrep:568
School not set Nigeria
30 July 2020

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peter
Peter answeredrep:1.4K
University of Lagos Nigeria
12 August 2020
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The nth term of an arithmetic progression is given by: Tn = a + (n - 1)d ------ eqn(1)

where a is the first term, d is the common difference, n is the number of term and Tn is the nth term.

for the 9th term,

T9 = a + (9 - 1)d

= a + 8d

Also, T9 = 499

Thus, a + 8d = 499 ---------- eqn(2)

for the 499th term,

T499 = a + (499 - 1)d

= a + 498d

Also, T499 = 9

Thus, a + 498d = 9 ---------- eqn(3)

eqn(2) and eqn(3) are simultaneous equations and can be simplified by elimination method.

Hence, subtract eqn(3) from eqn(2)

(a - a) + (8 - 498)d = (499 - 9)

-490d = 490

divide both sides by -490

d = -1

substitute d = -1 into eqn(2)

a + 8(-1) = 499

a - 8 = 499

Add 8 to both sides

a = 499 + 8

a = 507

Also, from eqn(1), to get the term which is equal to zero, Tn = 0.

That is, 0 = a + (n - 1)d

0 = 507 + (n - 1)(-1)

0 = 507 - n + 1

0 = 508  - n

n = 508

Ans a

 

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