Question

Find the following sums ?

a) 1+2+3+4 +5+.......................+100

b) 3+6+ 9+12+15+...................+300​

Answer 1

a) a1 = 1

d = 2-1 = 1

an = 100

So,,,,,,

an = a + (n-1)d

100 = 1+(n-1)1

99 = n-1

n = 100

Hence,,,,,

Sn = n/2(a+an)

= 100/2(1+100)

= 50×10

= 5050

b) a1 = 3

d = 6-3 = 3

an = 300

So,,,,,

an = a+(n-1)d

300 = 3+(n-1)(3)

297 = 3n - 3

300 = 3n

n = 100

Hence,,,,,,,,

Sn = n/2(a+an)

Sn = 100/2(1+300)

Sn = 50 × 301

Sn = 15050

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