Question

The sum of the first 10 items of an arithmetic sequence is 350 and the sum of the first 5 terms is 100.write the algebraic expression for the sequence.

Answer 1

The given is
S10 = 350 = n/2*[2a + (n-1)*d]

350 = 10/2 *[2a + (10-1)d]
350 = 5[2a + 9d]
350/2 = 2a + 9d
70 = 2a + 9d ...........(1)

also it is given that
S5 = 100 = 5/2 [2a + (5-1)*d]
100*2/5 = 2a + 4d
40 = 2a + 4d ............(2)


so from equation (1) and (2)
we get the value of a and d

a = 6
d = 7
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Answer 2

Given:-

sum of 10 term =350

a+9d=350 ----(i)

sum of 15 term=750

a+14d=750-------(ii)

so, subtracting (i) from(ii) ,we get..

$\frac{a + 14d = 750}{a + 9d = 350} \\ \\ 0 + 5d = 400 \\ \\ 5d = 400 \\ d = \frac{400}{5} \\ d = 80$

d=80------(iii)

putting the value of eq.iii in eq. i

a+9d=350

a+9*80=350------(in place of d we put the value of a+720=350.

which is given in the equation

. iii)

a=350-720

a= -370.

so now we find the value of 'a' and 'd'

now by using these values we can find 8th term.

$a8= a + (8 - 1)d \\ a8= a + 7d \\ a8= - 370 + 7 \times 80 \\ a8= - 370 + 560 \\ a8 = 190$

so your answer will be

8th term⏩ 190..............✔️✔️✔️✔️

#hope it will help you#