Question

If the sum of 8 terms of an A.P. is 64 and the sum of 19 terms is 361, find the sum of n terms.

Answer 1

Answer:

hi..mate here is your answer...

$s_{8} = 64 \\ s_{19} = 361 \\ s olve = \\ s_{8} = \frac{8}{2} (2a + (8 - 1)d) \\ 64 = 4(2a + 7d) \\ \frac{64}{4} = 2a + 7d \\ 16 = 2a + 7d.......eq1 \\ s_{19} = \frac{19}{2} (2a + (19 - 1)d) \\ 361 = \frac{19}{2} (2a + 18d) \\ 361 = \frac{19}{2} (2(a + 9d)) \\ 361 = 19a + 171d.....eq2 \\ solve \: \: \: eq1 \: \: \: \: and \: \: \: eq2 \\ 2a + 7d = 16 \\ 2a + 18d = 38 \\ d = 2 \\ from \: eq1 \\ 2a = 16 - 7(2) \\ 2a = 16 - 14 \\ 2a = 2 \\ a = 1 \\ so ...sum \: of \: n \: terms.... \\ s_{n} = \frac{n}{2} (2a + (n - 1)d) \\ s_{n} = \frac{n}{2} (2 + dn - d) \\ s_{n} = \frac{n}{2} (2 + 2n - 2) \\ s_{n} = \frac{n}{2} \times 2n \\ s_{n} = {n}^{2}$

hope my answer helps you ..

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