Question

# If the seventh term of an A.P. is 19 and its ninth term is 17, find its (63)rd term.

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Solution

## Nth term = a+ ( n-1 ) d ( where a is the first term, n is the no. of terms and d is the difference between two consecutive terms . ) seventh term = a7= 19 ninth term = a9 = 17 a7 = a + 6d ( Eq 1 ) a9= a+ 8d ( Eq 2 ) by subtracting ( 1 ) from ( 2 ) ⇒a+8d−a−6d=17−19 ⇒2d=263⇒d=163 by putting value of d in Eq. ( 2 ) a + 8×163=17 a + 863=17 a = 17−863 a = 163 a63 = a + 62d = 163+62×163 = 163 + 6263 = 1 ans.

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