Question

The 5th and 15th terms of an A.P. are 13 and - 17 respectively. Find the sum of first 21 terms of the A.P.

Answer 1

Answer:

$given = a_{5} = 13 \: \: \: and \: \: \: a_{15} = - 17 \\ too \: find = s_{21} = \: \: \\ solve = \\ a + 4d = 13......eq1 \\ a + 14d = - 17...eq2 \\ solve \: eq \: 1 \: \: \: and \: \: \: eq2 \\ d = - 3 \\ from \: eq1... \\ a = 13 - 4( - 3) \\ a = 13 + 12 \\ a = 25 \\ then... \\ s_{21} = \frac{21}{2} (2 \times 25 + (21 - 1)( - 3)) \\ s_{21} = \frac{21}{2} (50 + ( - 60)) \\ s_{21} = \frac{21}{2} ( - 10) \\ \\ s_{21} = 21 \times - 5 \\ s_{21} = - 105$

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