Question

The fi rst and the last term of an A.P. are 4 and 304 respectively and sum of n terms of the A.P. is 15554.

Find the number of terms and common diff erence.​

Answer 1

Answer:

number of terms(n)=101 and common difference (d)=3

Step-by-step explanation:

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Answer 2

★Given:-

• First term = 4
• Last term = 304
• Sum of n terms of the A.P. = 15,554.

★To find:-

Number of terms, common difference.

★Solution:-

To find the sum of n terms, we use the formula,

$\boxed{\rm S_n=\dfrac{n}{2}(a+l)}$

• a is first term
• l is last term
• $\rm S_n$ is sum of the terms.
• n is the number of terms.

Using this formula here,

$\leadsto\rm S_n=\dfrac{n}{2}(a+l)$

$\leadsto\rm 15554=\dfrac{n}{2}(4+304)$

$\leadsto\rm 15554=\dfrac{n}{2}(308)$

$\leadsto\rm n=\dfrac{15554 \times 2}{308}$

$\bullet\leadsto\bf n=101$

To find the last term of an A.P. we use the formula

$\boxed{\rm l=a+(n-1)d}\qquad\qquad ...[\rm where, \ d \ is \ the \ common \ difference,]$

Using this formula here,

$\leadsto\rm l=a+(n-1)d$

$\leadsto\rm 304=4+(101-1)d$

$\leadsto\rm 304-4=(100)d$

$\leadsto\rm 300=100d$

$\leadsto\rm \cancel{\dfrac{300}{100}}=d$

$\bullet\leadsto\boxed{\bf d=3}$

Hence, the common difference and number of terms are 3 and 101 respectively.