We read your photo as:

Given an arithmetic sequence with the first term a = 6 and the 20th term T20 = 82.

Mathematics

ScanSolve AI Answer

Answers

3 parts
a

d=4d = 4

b
402
c

The 56th term\text{The 56th term}

Step-by-step solution

6 steps

Here's how to solve this problem:

Given an arithmetic sequence with the first term a=6a = 6 and the 20th term T20=82T_{20} = 82.
The formula for the nn-th term of an arithmetic sequence is Tn=a+(n−1)dT_n = a + (n-1)d.

Part a· 2 steps

Find the common difference dd.

  1. Substitute the given values into the formula for T20T_{20}.

    T20=a+(20−1)dT_{20} = a + (20-1)d 82=6+19d82 = 6 + 19d

  2. Solve for dd.

    82−6=19d82 - 6 = 19d 76=19d76 = 19d d=7619d = \frac{76}{19} d=4d = 4

    Answer: d=4\boxed{d = 4}

Part b402

Find the 100th term.

  1. Use the first term a=6a=6 and the common difference d=4d=4 to find T100T_{100}.

    T100=a+(100−1)dT_{100} = a + (100-1)d T100=6+(99)4T_{100} = 6 + (99)4

  2. Calculate the value.

    T100=6+396T_{100} = 6 + 396 T100=402T_{100} = 402

    Answer: 402\boxed{402}

Part c

The 56th term\text{The 56th term}

Which term of this sequence equals 226?

  1. Set Tn=226T_n = 226 in the formula Tn=a+(n−1)dT_n = a + (n-1)d.

    226=6+(n−1)4226 = 6 + (n-1)4

  2. Solve for nn.

    226−6=(n−1)4226 - 6 = (n-1)4 220=(n−1)4220 = (n-1)4 2204=n−1\frac{220}{4} = n-1 55=n−155 = n-1 n=55+1n = 55 + 1 n=56n = 56

    Answer: The 56th term\boxed{\text{The 56th term}}

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA geometric sequence has first term a = 3/128 and sixth term T6 = 3/4. Find the common ratio and the…QConsider the arithmetic sequence 7, 12, 17, 22, ... a) Find the first term and common difference. b)…QFind the sum of the first 20 terms of the arithmetic progression: 2, 5, 8, extand so on.QGiven the arithmetic sequence 6, 10, 14, 18, ..., find the formula for the n-th term and the sum of…QThe sum of the first five terms of an arithmetic progression is 5. The sum of the next ten terms is…
Browse by topic:Pre-Calculus
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp