Question

8th term of an arithmetic sequence is 56. Find the sum of first 15 terms

Answer 1

Step-by-step explanation:

Sum upto 15 terms= 840 okkkkkkkkkkkkkk

Answer 2

Answer:

The sum of first 15 terms of the Arithmetic Progression = 840

Step-by-step explanation:

Given,

8th term of an arithmetic sequence = 56

To find,

The sum of first 15 terms

Solution:

Recall the formula

The nth term of an AP = aₙ = a+(n-1)d

The sum to n terms of an AP = Sₙ = $\frac{n}{2}(2a+(n-1)d)$,

Where 'a' is the first term and 'd' is the common difference of the AP.

Since it is given the 8th term of the AP is 56,

a₈ = a+7d = 56 ---------------(1)

Sum to 15 terms of the AP,

S₁₅ = $\frac{15}{2}(2a+(15-1)d)$

= $\frac{15}{2}(2a+14d)$

= $\frac{15}{2}X2(a+7d)$

= 15(a+7d)

Substituting the value of a+7d from equation (1) we get,

S₁₅ = 15× 56

= 840

The sum of first 15 terms of the Arithmetic Progression = 840

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