GP

FIND THE SUM TO N TERMS OF THE FOLLOWING SERIES 3+7+14+27+52+...

4 Answers

Writing down the differences....

3+7+14+27+521
4, 7, 13, 25
3, 6, 12

So the 2nd difference is a GP
and we can say that (t₃-2t₂+t₁) =3
and similarly the r^th 2nd difference is

now can u try from here on?

sum=3+7+14+27+52+...

= (3*1+0) + (3*2+1) + (3*4+2) + (3*8+3) + (3*16+4) +...+(3*2^n-1+(n-1))

= 3*(1+2+4+...+2^n-1 ) + (0+1+2+3+...+(n-1))

=3*(2^n-1-1) +(n-1)n/2

is my soln correct?

obviously :)

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