Determine the 25^{th} term of an A.P. whose 9 | vedclass

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(C) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d$.Giv

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(C) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d$.Given that the $9^{th}$ term $a_9 = -6$ and the common difference $d = \frac{5}{4}$.Substituting these values into the formula:$a_9 = a + (9 - 1)d$$-6 = a + 8 	imes \left(\frac{5}{4}ight)$$-6 = a + 2 	imes 5$$-6 = a + 10$$a = -6 - 10 = -16$.Now,we need to find the $25^{th}$ term $(a_{25})$:$a_{25} = a + (25 - 1)d$$a_{25} = -16 + 24 	imes \left(\frac{5}{4}ight)$$a_{25} = -16 + 6 	imes 5$$a_{25} = -16 + 30 = 14$.Thus,the $25^{th}$ term is $14$.

Determine the $25^{th}$ term of an $A.P.$ whose $9^{th}$ term is $-6$ and the common difference is $\frac{5}{4}$.

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