First slide

Arithmetic progression

Question

If for every $n \in N,$ , sum to n terms of an A.P. is $5 n^{2} + 7 n$ then its 10th term is

Moderate

A

7/2
B

570
C

102
D

52

Solution

We have $\begin{array}{l} a_{r} = S_{r} - S_{r - 1} \\ \Rightarrow a_{10} = S_{10} - S_{9} \\ = 5 (10^{2} - 9^{2}) + 7 (10 - 9) \\ = 102 \end{array}$

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