(A) Given: First term $a = 5$,common difference $d = 3$,and $n^{th}$ term $T_n = 50$.Step $1$: Find $n$ using the formula $T_n = a + (n - 1)d$.$50 = 5

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(A) Given: First term $a = 5$,common difference $d = 3$,and $n^{th}$ term $T_n = 50$.Step $1$: Find $n$ using the formula $T_n = a + (n - 1)d$.$50 = 5 + (n - 1)3$$45 = (n - 1)3$$15 = n - 1$$n = 16$.Step $2$: Find the sum of $n$ terms $S_n$ using the formula $S_n = \frac{n}{2}(a + T_n)$.$S_{16} = \frac{16}{2}(5 + 50)$$S_{16} = 8 \times 55$$S_{16} = 440$.Thus,$n = 16$ and $S_n = 440$.

Class 10 Mathematics Arithmetic Progressions Mix Examples - Arithmetic Progressions

Medium

With respect to the usual notations of an $A.P.$,if $a=5, d=3$ and $T_n=50$,find $n$ and $S_n$.

A
n=$16$,S_n=$440$
B
n=$15$,S_n=$440$
C
n=$16$,S_n=$420$
D
n=$15$,S_n=$420$

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Mix Examples - Arithmetic Progressions

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With respect to the usual notations of an $A.P.$,if $a=5, d=3$ and $T_n=50$,find $n$ and $S_n$.

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The sums of $n$ terms,$2n$ terms,and $3n$ terms of an $A.P.$ are $S_1, S_2,$ and $S_3$ respectively. Prove that $S_3 = 3(S_2 - S_1)$.

For the finite $A.P.$ $3, 8, 13, \ldots, 253,$ find the $20^{th}$ term from the end.

The $10^{th}$ term of an $A.P.$ is $52$ and its $17^{th}$ term exceeds its $13^{th}$ term by $20$. Find the $A.P.$ and also its $30^{th}$ term.

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Verify that each of the following is an $AP$,and then write its next three terms.
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