Question

The 99th term of the series 2+7+14+23+34+............... a)9999 b)9998 c)10000 d)9929

Answer 1

Given series,
2+7+14+23+34+...............................
7-2=5

14-7=7

23-14=9

34-23=11
we observe that difference between two successive terms is an another series that is, series of odd number starting from 5.
So we will find sum of those differences between two terms starting 5th to 6th term.
Difference between 5th and 6th term will be 13.
Series of odd number forms an AP.
34+sum of 94 odd numbers, 13 as a first term= 99th term of given series.
Sn=n/2{2a+(n-1)d}

S94=94/2{2(13)+(93)2}

S94=47{26+186}

S94=9964

Hence 99th term of given series=34+9964=9998