If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence an is given by:
an = a1 + ( n -1 ) * d
a1 = 5
a100 = a1 + ( 100 - 1 ) * d = - 292
a100 = 5 + 99 d = - 292
5 + 99 d = - 292 Subtract 5 to both sides
5 + 99 d - 5 = - 292 - 5
99 d = - 297 Divide both sides by 99
d = - 297 / 99 = -3
d = - 3
an = a1 + ( n -1 ) * d
a50 = 5 + ( 50 -1 ) * d
a50 = 5 + 49 * d
a50 = 5 + 49 * ( - 3 )
a50 = 5 - 147
a50 = - 142
If the first term of an AP is 5 and it's 100th term is -292.find it's 50th term.
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