The 3^{rd} and 7^{th} term of an arithmetic p | vedclass

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(C) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an arithmetic progression is given by $t_n = a + (n-1)d$.Given:$t

Vedclass · Accepted Answer

$51$

Vedclass · Answer

(C) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an arithmetic progression is given by $t_n = a + (n-1)d$.Given:$t_3 = a + 2d = -9$  --- (Equation $1$)$t_7 = a + 6d = 11$  --- (Equation $2$)Subtracting Equation $1$ from Equation $2$:$(a + 6d) - (a + 2d) = 11 - (-9)$$4d = 20$$d = 5$Substituting $d = 5$ into Equation $1$:$a + 2(5) = -9$$a + 10 = -9$$a = -19$Now,finding the $15^{th}$ term $(t_{15})$:$t_{15} = a + 14d$$t_{15} = -19 + 14(5)$$t_{15} = -19 + 70$$t_{15} = 51$

The $3^{rd}$ and $7^{th}$ term of an arithmetic progression are $-9$ and $11$ respectively. What is the $15^{th}$ term?

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