The 1st and last terms of an AP are -3 and 25 and their sum of all the terms are 1837. Calculate the number of tetms, the common difference and the middle term.
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Given that
Step-by-step explanation:
a = -3 and an= 25 and Sn= 1837
So Sn= n/2(a+an)
1837= n/2(-3 + 25)
1837=n/2 (22)
1837= 11n
n= 1837/11 = 167
Thus number of terms are 167
We know
an= a + (n-1)d
25= -3 + (167-1)d
28 = 166d
d= 28/166 = 14/83
Middle term = (a + an)/2 = (25-3)/2 = 11
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