Question

find the sum of all odd natural number from 1 to 150

Answer 1

1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41+43+45+47+49+51+53+55+57+59+61+63+65+67+69+71+73+75+77+79+81+83+85+87+89+91+93+95+97+99+101+103+105+107+109+111+113+115+117+119+121+123+125+127+129+131+133+135+137+139+141+143+145+147+149 = 5625
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Answer 2

hi..

A.P. = 1 + 3 + 5 + ...................+ 149

here,

a = 1

d = 2

l = 149

first we will find,

a(n) = 149

a + (n-1)d = 149

1 + (n-1) 2 = 149

n-1 = 148/2

n = 74 + 1 = 75

so,

n = 75

sum of n terms = n/2 [2a + (n-1)d]

$s(75) = \frac{75}{2} (2 \times 1 + 74 \times 2)$

$sum = \frac{75}{2} (2 + 148)$

$\frac{75}{2} (150)$

$75 \times 75$

$\bold{ \underline{sum = 5625}}$

$\huge{thank \: u}$