Question

Find the sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 +…

Answer 1

Answer:

Given, series: 1+4+6+5+11+6.... is a combination of two AP's i.e.,

(1+6+11+.....)+(4+5+6......)

Now, each of the AP will have 100 terms.

⟹S=S

1

+S

2

whereS

1

=1+6+11...andS

2

=4+5+6...

Now,S

1

=

2

n

[2a+(n−1)d]=

2

100

[2×1+(100−1)(5)]

⟹S

1

=50(497)=24850

Again,S

2

=

2

n

[2a+(n−1)d]=

2

100

[2×4+(100−1)(1)]

⟹S

1

=50(107)=5350

∴S=S

1

+S

2

=24850+5350=30,200

Hence, the sum of 200 terms to the given series is 30,200.

Step-by-step explanation:

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