In an AP the first trem is 12 and c.d is 16 .if the last term of the AP is 252 find its middle term

In an AP the first trem is 12 and c.d is 16 .if the last term of the A

1.	In an AP the first trem is 12 and c.d is 16 .if the last term of the AP is 252 find its middle term
Answer» a8= a + 7d =12+7×16 =12+112 =124\xa0 The Question Should be "In an AP the first trem is 12 and c.d is 6. if the last term of the AP is 252 find its middle term"Ans.\xa0First Term a = 12\xa0Commond Difference d = 6Last term an\xa0= 252We know\xa0=> an = a + (n-1)d=> 252 = 12 + (n-1)6\xa0=> 240 = (n-1)6=> 40 = n -1\xa0=> n = 41\xa0Total Number of terms = 41\xa0Middle term =\xa0{tex}({n+1\\over 2 })^{th} term = ({41+1\\over 2 })^{th} term = 21^{th} term{/tex}a21\xa0\xa0= 12\xa0+ (21-1)6=> a21\xa0= 12 + 120 = 132 First term(a) =12 Last term(l) =252l = a+(n-1)d252 = 12+(n-1)252 = 12+16n-16256 = 16n\xa0n = 16n/2 = 16/2 = 8So, middle term is 8.\xa0