Question

Q. If the nth of an AP -1,4,9,14...........is 129 . Find the value of n.
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Answer 1

Answer:

$\huge{ \purple{ \star{answer}}}\\ \\ -1,4,9,14...........129 \\ \\ a = - 1 \\ \\ d = 4 - ( - 1) = 5 \\ \\ tn = 129 \\ \\ \huge{ \pink{to \: \: \: find : }} \: \: n \\ \\ \large{ \bold{tn = a + (n - 1)d}} \\ \\ \large{ \bold{129 = - 1 + (n - 1)5}} \\ \\ \large{ \bold{130 = 5n - 5}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large{ \bold{135 = 5n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large{ \bold{ \frac{135}{5} = n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large{ \bold{27 = n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Answer 2

${\huge{\underline{\underline{\sf{\pink{Required \: answer:-}}}}}}$

Given:

• -1,4,9,14...........129

a=−1

d=4−(−1)=5

tn=129

To Find:

tn=a+(n−1)d

129=−1+(n−1)5

130=5n−5

135=5n

$n = \frac{135}{5}$

27=n