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if the seventh term of an AP is 1/9 of its ninth term is 1/7find its 63rd term
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find its 63rd term
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We know that nth term of an AP an = a + (n - 1) * d.
Given that a7 = a + (7 - 1) * d
= a + 6d
a + 6d = 1/9 ---------- (1)
Given that a9 = a + (9 - 1) * d
= a + 8d
a + 8d = 1/7 ------------- (2)
On solving (1) & (2), we get
8d - 6d = 1/7 - 1/9
2d = 9 - 7/63
2d =2/63
d = 1/63
Substitute d = 1/63 in (1), we get
a + 6(1/63) = 1/9
a + 6/63 = 1/9
a = 1/9 - 6/63
a = 1/63
Now,
63rd term = a + (63 - 1) * d
= 1/63 + (62) * 1/63
= 1 + 62/(63)
= 63/63
= 1.
Therefore 63rd term of an AP is 1.
Hope this helps!
Given that a7 = a + (7 - 1) * d
= a + 6d
a + 6d = 1/9 ---------- (1)
Given that a9 = a + (9 - 1) * d
= a + 8d
a + 8d = 1/7 ------------- (2)
On solving (1) & (2), we get
8d - 6d = 1/7 - 1/9
2d = 9 - 7/63
2d =2/63
d = 1/63
Substitute d = 1/63 in (1), we get
a + 6(1/63) = 1/9
a + 6/63 = 1/9
a = 1/9 - 6/63
a = 1/63
Now,
63rd term = a + (63 - 1) * d
= 1/63 + (62) * 1/63
= 1 + 62/(63)
= 63/63
= 1.
Therefore 63rd term of an AP is 1.
Hope this helps!
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