Noo solve the problem in English NOT KISWAHILI

Languages

ScanSolve AI Answer

Here is the solution to (a) in English:

1. (a) An arithmetic sequence is composed of numbers exactly divisible by 4, with the last number being 928. The first number is 4.

  • Step 1: Determine the common difference. Since all numbers in the sequence are exactly divisible by 4, the common difference between consecutive numbers must be 4.

    d=4d = 4

    The common difference is 4\boxed{\text{4}}.

  • Step 2: Determine the number of terms in the series. We use the formula for the nn-th term in an arithmetic sequence: L=a+(n−1)dL = a + (n-1)d. We have L=928L = 928, a=4a = 4, and d=4d = 4.

    928=4+(n−1)4928−4=(n−1)4924=4(n−1)9244=n−1231=n−1n=231+1n=232\begin{align*} 928 &= 4 + (n-1)4 \\ 928 - 4 &= (n-1)4 \\ 924 &= 4(n-1) \\ \frac{924}{4} &= n-1 \\ 231 &= n-1 \\ n &= 231 + 1 \\ n &= 232 \end{align*}

    The number of terms in the series is 232\boxed{\text{232}}.

  • Step 3: Determine the sum of all terms. We use the formula for the sum of an arithmetic series: Sn=n2(a+L)S_n = \frac{n}{2}(a + L). We have n=232n = 232, a=4a = 4, and L=928L = 928.

    S232=2322(4+928)S232=116(932)S232=108112\begin{align*} S_{232} &= \frac{232}{2}(4 + 928) \\ S_{232} &= 116(932) \\ S_{232} &= 108112 \end{align*}

    The sum of all terms is 108,112\boxed{\text{108,112}}.

  • Step 4: Determine the 80th term. We use the formula for the nn-th term: an=a+(n−1)da_n = a + (n-1)d. We want to find the 80th term, so n=80n = 80. We have a=4a = 4 and d=4d = 4.

    a80=4+(80−1)4a80=4+(79)4a80=4+316a80=320\begin{align*} a_{80} &= 4 + (80-1)4 \\ a_{80} &= 4 + (79)4 \\ a_{80} &= 4 + 316 \\ a_{80} &= 320 \end{align*}

    The 80th term is 320\boxed{\text{320}}.

Was this helpful?

Still stuck on this one?

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

Got a different question?Ask your own question
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