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Is -150 a term of AP 17,12,7,2

Posted by Alok Raj 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

The given term of arithmatic progression is17, 12, 7, 2, ......
Here, a = 17, d = 12 - 17 = - 5 where a is first term and d is common difference
Suppose a_n = -150
a + (n - 1)d = -150 {tex}\Rightarrow{/tex} 17 + (n - 1)(-5) = -150
{tex}\Rightarrow{/tex} (n - 1)(-5) = -150 - 17 {tex}\Rightarrow{/tex} (n - 1)(-5) = -167
{tex}\Rightarrow{/tex} n - 1 = {tex}\frac { 167 } { 5 }{/tex} {tex}\Rightarrow{/tex} n = {tex}\frac { 167 } { 5 }{/tex} + 1
{tex}\Rightarrow{/tex} n = {tex}\frac { 167 + 5 } { 5 } = \frac { 172 } { 5 } = 34 \frac { 2 } { 5 }{/tex}where
n is not a whole number.
{tex}\therefore{/tex} -150 is not a term of the A.P.

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