Find n and d where a=8 , a_n=62 ,S_n=210.

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Solution

We know that Sn= (n/2)[a + l] where l is the last term or nth term
Hence 210 = (n/2)[8 + 62]
210 = (n/2)[70]
35n = 210
Therefore, n = 6
Recall an= a + (n - 1)d
Tht is 62 = 8 + 5d
54 = 5d
∴ d = 54/5

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(vi) n and $a_{n}$ , if a = 2, d=8 and $S_{n}$ =90.
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(viii) $S_{22}$ , if d =22 and $a_{22}$ =149