Quant · Algebra

Sequences and Series

4 sub-topics · 50 lessons · 81 questions · 18 PYQs

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Arithmetic Progression13 lessons · 25 questions · 7 PYQs

Geometric Progression18 lessons · 25 questions · 5 PYQs

Special Series14 lessons · 24 questions · 6 PYQs

AGP, HP and Means5 lessons · 7 questions

Formula sheet

n-th term of a GP
$T_n = ar^{n-1}$
n-th term of an AP
$T_n = a + (n-1)d$
Term from consecutive sums
$T_n = S_n - S_{n-1}\ (n\ge 2)$
Equal sums of an AP
$S_m = S_n \Rightarrow S_{m+n} = 0$
Sum of an infinite GP
$S_\infty = \frac{a}{1-r}\ (|r|<1)$
Sum of the first n terms of a GP
$S_n = \frac{a(r^n-1)}{r-1}\ (r\ne1)$
Sum identities of an AP
$S_p=q,S_q=p\Rightarrow S_{p+q}=-(p+q)$
n-th term when the sum formula is given
$t_n = S_n - S_{n-1}\ (n\ge2),\ t_1=S_1$