The first and sixth term of GP is 2 and 486.Find the sum of its first six terms ?
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the sum of its first six terms is 728
Rajagiri:
I need it with brief explanation
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The first term be a and the common ratio be r.
Now the term 1 = 2
or, ar^n-1 = 2
or, ar^1-1 = 2
or, ar^0 = 2
or, a = 2
Now, Term 6 = 486
or, ar^n-1 = 486
or, 2r^6-1 = 486
or, r^5 = 243
or, r^5 = 3^5
or, r = 3
Therefore now the terms would be 2,6,18,54,162 and 243.
There sum is 728
Now the term 1 = 2
or, ar^n-1 = 2
or, ar^1-1 = 2
or, ar^0 = 2
or, a = 2
Now, Term 6 = 486
or, ar^n-1 = 486
or, 2r^6-1 = 486
or, r^5 = 243
or, r^5 = 3^5
or, r = 3
Therefore now the terms would be 2,6,18,54,162 and 243.
There sum is 728
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