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Iteru [2.4K]
1 year ago
5

Find the sum of the first 16 terms of an arithmetic sequence where a4=7 and a7= 16. (I need the procedure y Example) please

Mathematics
1 answer:
Luden [163]1 year ago
6 0

Answer:

S₁₆ = 328

Step-by-step explanation:

the nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 7 and a₇ = 16 , then

a₁ + 3d = 7 → (1)

a₁ + 6d = 16 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 3d = 9

3d = 9 ( divide both sides by 3 )

d = 3

substitute d = 3 into (1) and solve for a₁

a₁ + 3(3) = 7

a₁ + 9 = 7 ( subtract 9 from both sides )

a₁ = - 2

the sum to n terms of an arithmetic sequence is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

with a₁ = - 2 and d = 3 , then

S₁₆ = \frac{16}{2} [ (2 × - 2) + (15 × 3) ]

     = 8(- 4 + 45)

     = 8 × 41

     = 328

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