Question

Find the value of 7 + 15 + 23 +...+ 767 + 775 + 783?

Answer 1

• The value of the given sum is 38710

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Given

The sum:

• 7 + 15 + 23 + ... + 767 + 775 + 783

We can notice that:

• Subsequence terms have the difference of 8,
• The first term is 7,
• The last term is 783.

Since the difference between subsequence terms is same, the terms form an arithmetic progression.

Use the nth term equation to find the number of terms:

• aₙ = a₁ + (n - 1)d

Use the given values and find n:

• 783 = 7 + (n - 1)*8
• 8(n - 1) = 776
• n - 1 = 776/8
• n - 1 = 97
• n = 98

Now use the equation for sum of the first n terms of AP:

• Sₙ = (a₁ + aₙ)*n/2

Substitute the values and calculate the sum:

• S₉₈ = (7 + 783)*98/2 = 790*49 = 38710