The 2nd and 5th term of a.p are -7 and 56 respectively find the first term. The common ratio. The sum of the five term

A student reads 45 pages in 2 h and x pages in 3 h.

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Find the sum of the following series

To find the first term (a) of an arithmetic progression (AP), we can use the formula:

a + (n - 1) * d = term

where 'n' is the term number and 'd' is the common difference.

Given that the 2nd term is -7, we have:

a + (2 - 1) * d = -7
a + d = -7 -- (equation 1)

Similarly, given that the 5th term is 56, we have:

a + (5 - 1) * d = 56
a + 4d = 56 -- (equation 2)

To solve these equations, we can use a method called 'elimination' or 'substitution.'

Elimination method:
Multiply equation 1 by 4, we have:

4a + 4d = -28 -- (equation 3)

Now, subtract equation 3 from equation 2:

(a + 4d = 56) - (4a + 4d = -28)

Simplifying, we get:

-3a = 84
a = -28

Hence, the first term (a) of the AP is -28.

To find the common difference (d), substitute the value of a (-28) into equation 1:

-28 + d = -7

Simplifying, we get:

d = -7 + 28
d = 21

Therefore, the common difference (d) of the AP is 21.

Finally, to find the sum of the five terms, we can use the formula:

Sum of AP = (n/2) * [2a + (n - 1) * d]

Given n = 5, a = -28, and d = 21, we substitute the values into the formula:

Sum = (5/2) * [2(-28) + (5 - 1) * 21]

Simplifying, we get:

Sum = (5/2) * [-56 + 4 * 21]
Sum = (5/2) * [-56 + 84]
Sum = (5/2) * [28]
Sum = 70

Therefore, the sum of the five terms in the AP is 70.

Use your definitions:

a+d = -7
a+4d = 56
subtract them:
3d = 63
d = 21

back in a+d=-7
a+21 = -7
a = -28

sum(5) = (5/2)(-56 + 4(21)) = 70
or
sum(5) = (5/2)(first + last)
= (5/2)(-28 + 56) = 70

check:
our terms are:
-28 -7 14 35 56 ---> add them up to get 70