Question

For a given arithmetic sequence, the 11ᵗʰ term, a_(11), is equal to 69 , and the 29ᵗʰ term, a_(29), is equal to 123. Find the value of the 76ᵗʰ term, a_(76).

Answer 1

term 76= 264

Step-by-step explanation:

term 11 = first term (a1) + 10r where r is the ratio

term 29 = a1+28r

69 = a1+10r and 123 = a1+28r

a1 = 69 -10r results 123 = 69+18r, 18r = 54, r =3 this means a1 = 69- 30 = 39

now we know a76 = a1 + 75r this means a76 = 39 + 225 = 264

Answer 2

The 76th term of the given arithmetic sequence, with the 11th term being 69 and the 29th term being 123, is 264. This is determined using the formula for the n-th term of an arithmetic sequence.

Step-by-step explanation:

To find the value of the 76th term, a_(76), in the given arithmetic sequence when the 11th term, a_(11) is 69 and the 29th term, a_(29), is 123, we need to use the formula for the n-th term of an arithmetic sequence, which is a_n = a_1 + (n - 1) × d, where a_1 is the first term and d is the common difference.

To find the common difference, we use the information provided: a_(29) = a_(11) + 18d, which means 123 = 69 + 18d. Solving this gives us d = 3.

Now we have the common difference and can find the first term using the 11th term formula: a_(11) = a_1 + 10d, which gives us 69 = a_1 + 10 × 3. Solving for a_1 gives a_1 = 39.

Finally, we use the formula for the n-th term to find a_(76): a_(76) = a_1 + 75d = 39 + 75 × 3 = 39 + 225 = 264. Therefore, the value of the 76th term is 264.