Answer:

>>> Mathematics

> 1765

Explain: It is known that the 3rd term is 154, meaning that the 1st term is a, the 2nd term is a + d, and the 3rd term is a + 2d. Therefore, we can write the equation as follows:

→ a + 2d = 154 (1)

It is also known that the sum of the 5th and 7th terms is 290, so we can write another equation as follows:

→ 2a + 6d = 290 (2)

To solve equations (1) and (2), we can use the elimination or substitution method. We will use the substitution method, solving equation (1) for a:

→ a + 2d = 154

→ a = 154 - 2d

We then substitute the value of a into equation (2):

→ 2a + 6d = 290

→ 2(154 - 2s) + 6s = 290

Simplify and solve the equation to find the value of d:

→ 308 - 4d + 6d = 290

→ 2d = 18

→ d = 9

After knowing the value of d, we can find the value of a by using equation (1):

→ a + 2d = 154

→ a + 2(9) = 154

→ a = 136

We now have the values for a and d, so we can use the formula to find the sum of the first 10 terms:

→ Sn = n/2 (2a + (n-1)d)

→ Sn = 10/2 (2(136) + (10-1)(9))

→ Sn = 5(272 + 81)

→ Sn = 5(353)

→ Sn = 1765

So, the sum of the first 10 terms of this arithmetic sequence is 1765 ✓

• 6 March 2023